I'm the last person who should be describing HST, but basically it is an automatic transmission type of thing. Basically, you have a rocker type foot pedal that when you push forward you go forward and when you rock it back you go in reverse. Super easy to drive. Great for using a front end loader and going back and forth, etc. But, as you can imagine, it ups the price a fair amount and diminished available horsepower. But, HST is very popular.
For your specific case, I would not advise a used tractor. I'm not against used as a rule but there are several things in your case that would recommend against it. First, it sounds like you are new to tractors. Just because its used doesn't mean its going to need constant wrenching, but it might need
some. Second, you are going to be a long way away a fair amount of time. You don't want to have to deal with malfunctions long distance, or spend your precious seat time wrenching. Third, your wife is probably not going to want to deal with a tractor that needs special care.
All of that assumes that because its used it is going to have problems. That is not a given by any stretch. But that's where number four comes in. Good, low hour used tractors are not cheap. If you have $10k in cash you might find what you want in a decent used. But if you are going to have to borrow any money at all, most of the major manufacturers offer 0% financing which gets you more tractor for less money.
As far as what to buy, you've gotten some good pointers. I don't know anything about New Holland or Massey. But you can't go wrong with them. I don't know anything about Kioti or Mahindra either, but likely to be good, affordable machines. I agree with others that you should look at 30-45 hp. I think an FEL (front end loader) is also a must. You will use it in more ways than you can imagine and it expands the functionality of your machine exponentially.
So, 30-45 hp and FEL. That means $10k is probably not going to do it in the new or shiny used market. At least it didn't for me and i looked pretty hard.
I have a Kubota
L4400, a very basic 45 hp, 4wd with FEL. It was about $19,000. The
L3400 can be had for less and is 30 hp, it comes in an HST model but that raises the price, of course. The John Deere 790 is comparable to the
L3400 but a bit less tractor all the way around, but for less money. The JD 990 is very comparable to the
L4400 and similarly priced. Those are the 'economy' tractors I looked at.
Where are you stationed? Pensicola? I was stationed at Eglin AFB. I now live in SC. Where is your place in SC?