where do I begin with climbing gear?

I dabbled in rock climbing when I was younger, but it wasn’t until last year that I really got into it. I climbed with my ex boyfriend who fortunately had extra shoes/harness that I used whenever we went climbing. We’re not together anymore and I own absolutely no climbing gear! I live in Miami which has zero outdoor climbing and the climbing gym I go lets me rent everything I need. However this summer I’ll be working in Teton National Park and I really w SHAREit ant to get some climbing done there! I’m kind of just wondering how I should go about buying everything I need, what I should start with, etc. I’m also wondering what kind of gear I’d be safe with buying used (if any) and what gear I should buy brand new??? Any advice would be greatly appreciated.UC Browser

REI has advice for you:

https://www.rei.com/learn/c/climbing

Harness, Helmet, Shoes, Chalk bag, belay/rapell device, some lockers and an anchor system, could also get a prusik cord for backing up rapells. Maybe get a set of quick draws as well. But not essential as I'm guessing you will be climbing with someone experienced that should have gear. 

In addition to the obvious, shoes harness halmet belay device, geta good 30 - 40 liter backpack so you can carry your fair share of the load.

The climbing in the tetons involves significant hiking and you will be expected to carry your personal climbing gear, extra clothing, food, water and at least a rope.  Clothing is going to include rain gear and insulation. 

The above suggestions are all good, and if you have that (and know how to belay, and are a good person to hang with) you shouldn't have any problem.

One good thing is that most folks who you'd want to climb with (at least as a beginner) will usually have gear (a rack and rope).

A lot of folks will disagree with me, but I buy a lot of stuff used.  Most of the time, it's pretty easy to inspect things: as long as nylon is new-ish looking then it's probably okay.  

Other folks think that the money you save there isn't worth the peace of mind they are losing in worrying about what might have been done with the gear before they had it.  

The normal compromise on that is to say that shoes/packs etc are easy to buy used and as you get to other stuff like harnesses and ropes it's not such a great idea.  But there is a lot of nice stuff that you can get used.

Working and climbing in the Tetons, or any other large area of trad and alpine climbing? Buy some good approach shoes for approaching (duh) and easy 5th class. Good trail runners are an option, but not as good climbing.

For your climbing shoes, understand that some climbers like a larger size than you might be using in the gym. Fit will be a more important factor than the “performance” of the shoe.

Awesome opportunity for you! A year from now you will be offering the advice. 

I’ll agree with pretty much everyone here, get a harness, shoes, chalk bag, belay device (atc), and helmet. A chord and a couple lockers for anchors wouldn’t hurt either. Find some people to climb with and teach you on their gear in case  you don’t like it you don’t have to hawk it later. As far as buying used goes you can get it all used safely, but a chord is cheap and probably best new. A helmet doesn’t ever hurt, but that’s all climber preference and you can find that dead horse all over the forums. Enjoy

John Reeve wrote: A lot of folks will disagree with me, but I buy a lot of stuff used.  Most of the time, it's pretty easy to inspect things: as long as nylon is new-ish looking then it's probably okay.  

A few years ago, I met someone who stored his climbing rope in the trunk of his car. Right next to an old car battery. Apparently, some people just never read manuals for gear they buy. Not even gear they put their life on. It is not always possible to see if nylon material has been compromised by chemicals. So, buying used life-saving equipment from an unknown source might not be a great idea. A whole bunch of years back, there was a rope that snapped apart in a gym somewhere. They traced it back to acid. So, simple rule is to buy nylon (or soft material) new, but you can get aluminum and steel (hard stuff) used.

Justin Sanger wrote: A helmet doesn’t ever hurt, but that’s all climber preference and you can find that dead horse all over the forums.

The area mentioned is the Tetons; an alpine environment somewhat known for crumbly rock. Many consider helmet optional at a single-pitch sport crag, but few would promote brainbucketless alpine adventures.

My suggestion:
New: Rope, harness, and anchor material (I would go with three 2-foot slings, but others might prefer PAS or similar).
Possibly used: belay device, three locking biners (one of which should work well with the belay device), shoes, helmet.
Optional: chalk bag.

Without knowing your skill level, I disagree with those suggesting buying anchor gear. First off the anchor gear won’t help you unless you are already doing lead climbing. In which case you’ll need a rack of quick draws in addition to rope and said anchor material.
More than likely you’ll be climbing with others that have all this gear.
For climbing with other more experienced folks in the mountains, get a helmet, harness, comfortable all around shoes like TC Pros or similar, chalk bag, tube type belay/rappel device, a pre made auto block or prussic,  a few lockers, a 30-40 liter pack, lightweight shell jacket, headlamp.
A rope wouldn’t hurt as you’ll eventually need it and you can offer yours to save wear on your new partners. A good 9.8 70 meter is good all around.
If you are not experienced at belaying then take a class. Wouldn’t hurt to take a lead class especially if they offer anchor building/take down.
The rest of the gear you’ll need is specific to the type of climbing you will expect to do in the future and you won’t know that till you gain experience.
If you can show competence in belaying, you’ll find someone to help mentor you to the next level. Then you can rely on their advice as to what gear you might start adding to your personal kit. For instance if you are doing mostly sport climbs, a set of a dozen quickdraws and some sport anchor gear us in order. Etc.
As for new or used. If you don’t know the history then consider any nylon items suspect. I have a bunch of ropes that were stored on my sailboat in a locker that look brand new. The problem is that I had a battery overheat and boil out in a nearby locker. This means there’s a possibility that sulfuric acid gases may have contacted the ropes making them dangerous to use. You would never know by looking. Hard gear like carabiners etc, provided they look cared for are likely good for years of use. 
Have fun, be safe. Don’t bit off more than you can chew. Remember that outdoors, small things have big consequences. Take the recent death of Brad Gobright for instance. A single missing safety knot on a rappel line was the difference between life and death.  Be humble, offer to carry some weight and pay for a tank of gas and the climbing community can be a welcoming group of folks. 

Cesar Cardenas wrote: The big ones are gonna be shoes, harness, chalkbag, a belay device, a helmet, a waterbottle or two, a jacket, and a backpack for all of this.

Good advice. And there's tons of advice if you search the web. 

I would say shoes are #1. Do you want to be renting smelly gym shoes? Are they going to fit as good as one you buy? The answer to both is no. Shoes stretch to fit your foot and as mentioned used may be smelly so don't buy used. You'll want an all around shoe that's comfortable enough to wear for a long climb, but tight enough to give good performance, so your big toe should be just a little bit bent when wearing them. Go to a store and try on everything in your size. Different brands and different models fit different. Find ones that fit YOUR feet. The rest of the stuff you can borrow/rent and it won't make a difference.

Then a chalk bag. And you are set to join someone to go bouldering. (if they have a pad)

Then a harness (you trust your life to it so not worth saving a few bucks to buy used IMO) and a belay device (ATC guide/ Petzl Reverso stye) a locking biner for it.  And you are set to join someone to roped climb.

Preferably also get a helmet (I like the Petzl meteor), a 2nd locking biner to connect yourself to an anchor with the rope.

Doubtful the OP is even reading these responses.

I‘ll second the point about getting a pack large enough to carry your share of gear, not just your own gear. When you’re brand new, it’s normal to have only personal gear and expect to use your more experienced partners’ rope/rack; it’s not ok to expect them to carry everything just cause they own everything. At the very least be prepared to strap the rope onto the outside of your pack, but better to just get a larger pack up front.