yts-62ii or 82z??

Hello danewsaxkid. Welcome to the forum. While the 62II tenor in silver plate is nice, the 82Z in silver plate is essentially a 62 on steriods. The 82Z has a richer sound from my experience. The silver Z will cost you about 3200.00. It's an awesome horn.

I think, and don't take me for a snob (I am sincerely trying to be helpful), that you won't find a difference in those 2 and you'll sound the same: since you are a beginner it's perfectly normal (we all were beginners some time ago).
So I'd suggest to spend your budget for the 62 plus a good mouthpiece to upgrade the not so good (in my opinion) stock one.
You'd do better with the 62 and a good mouthpiece than with the 82Z and the stock one.
Also make sure you have some $$$ left for lessons.
Those are your picks but if you have the chance I suggest you to try the Yanagisawa 901: I own it and prefer to the 62 and 82Z I used to own sometime ago. Unfortunately Yanagisawas are not as easy to come by as Yamahas.

Just my opinion of course (no truths here, just opinions ).

Eeny Meny Miny Moe

I have to agree with RISPOLI on this one. There will not be much difference (if any) between the 62II and the 82z at this point in your playing life. The 62II will save you a couple bucks (that you can use for a good mouth piece and some lessons). Both horns are beauties (Silver or not), and you really can't go wrong with either horn. There is something to be said about starting with the best, so you can't blame anything bad on the equipement. But, I love my 62II, and you will too.......

The Z is alot better sounding sax. Alot warmer and fuller sounding. 62s can be very neutral sounding which some people take as being very dry sounding. Z has more overtones and richness to the sound.

My 11 year old tenor player liked the Z better than the 62. She plays a SX-90 Keilwerth in lacquer.

My input Custom Z's are a overall nicer horn: The sound overall is deeper and richer and the detailing is crazy on it. It's a nicer presentation horn also. When I wanted a new sax, I was choosing between a Ref. 54, a Yani A902, and a black lacquer Custom Z. The Yani and Custom Z was a close tie. Custom Z's are in my opinion better for performance over the 62ii. I'm not sure what you're into, but I think the extra money would be worth it.