I would definitely resist the urge to buy a pretty, shiny new horn that is a cheap piece of crap. A pitfall many a beginner falls into. It is vital that you get a solid, quality horn regardless of the cosmetic niceties of it. This is paramount.
I mention this because the above vendor link, including many other online music stores, have an abundance of these cheap horns within their lower price range offerings that are not anything approaching the quality and suitability of a good used horn for the same amount of money.
Absolutely ! Beware of ANY tenor which is new and costs under $900.....it's pretty much guaranteed to be bad.
Here's my advice, part I:
1) You have $349.
2) You are 11 years old.
~ Stay away from eBay. Only experienced eBayers should use eBay when buying a musical instrument.
I do not say this to offend you, but to help.
The problem with eBay horns is...90% of them require repair work after you receive 'em. I can pretty much guarantee a 99.5% likelihood that any Tenor on eBay which sells for $350 or less will need $150-500 of professional tech work.
Looking at the auctions you initially listed...the first one ended over $400, plus shipping you are at almost $450. So that isn't a Tenor for $350.
The second auction has these magical words, very politely inserted into the description:
"This tenor was recently re-padded, regulated and currently plays very nicely. That said, I would still encourage you to budget for a visit to your repair person to have the horn set-up to your particular standards"
You might think this means when you take the horn out of the case, it will play up and down with no issues. That would be a bad assumption.
The seller has included "wiggle words" to cover their butt. They are telling you the horn will need some tech work when you receive it, and do not buy it if you do not have the money budgeted for additional tech work.
Then if you look at the Return Policy section of the auction....voila !...the seller does not accept returns.
So, at the end of the day...this will NOT be a $350 Tenor, either.
Pretty sneaky, eh ?
Piece of advice Part II:
~ You and your parents need to increase your budget just a bit..... if what you want is to buy a playing, quality Tenor sax. $350 can get you a VERY good Alto in good shape, but not a Tenor.
If you have a tad over $400...then you have a lot of options available to you for a good, solid, playing, used horn which will last your for a decade or more.
$350 just won't get you there. Do you think you and your family can muster another $75 ??
Because I, for one...and likely a few other sellers/members here on this Forum, can sell you a good, working Tenor for $425 shipped which would NOT need add'l work once you got it.
Yes, it's an under-market-value price....but.... having been hanging around here for a while, I can say that there are several of us (adults) who will gladly give a young player a break on a solid horn because, well...this is a Sax Community...and that's what older folks do for younger folks with limited means, sometimes.
If you posted in the "Wanted" section stating just that ("I need an appropriate Tenor sax for an 11 y.o. beginner for $425 shipped. It has to be in decent shape and playable with no issues requiring repair")...I bet you'd get some replies.