I love these questions! I've had horses since 1985, and I spent 12 years--in a GOOD economy--looking for the right place. It should be easier today, if you are solvent, but I have a few things for you to consider, and advice.
First, don't buy a swamp. Look for places that suit you today, then go back in the early/mid-Spring and see what they look like after a heavy rain. Most of us don't have the resources to buy a place with an indoor arena, so you will want to be able to ride your property. I own 5 acres. My DH's heart bypass Dr. owns 80 acres ~ 10 miles away from me, and in the rainy season, most of it is a perpetual, wooded lake. My property was the first built in our tiny town, ~100 years ago, and it drains east, though we're so flat it's hard to tell, EXCEPT after heavy rains. My former farm property drains very well. We have PLENTY of riding space ON the property, and the owner's permission to ride the farm fields behind us in between crops. ALWAYS get permission before attempting it and ticking off the owner.
Second, don't buy less than 2 acres, unless you plan to build that indoor arena for ALL of your training. Don't buy too much, either. You'll have to maintain or, even build fencing and then, maintain that. The exception is wooded areas, but you'll want to walk them with a "fine toothed comb" for any previous barbed wire fencing. My 19 TWH found a piece of that while riding in Shawnee National Forest a few years ago. Big property upkeep is time consuming and takes away from your time with your horses. I have kept up to 5 horses on my property, and generally they graze the 4 acres of turnout from April to November. That takes a big bite out of $ for hay.
Third, ZONING. You probably will want to live out your days there once you get your Dream Place, so make sure that you are zoned for horses before you are stuck with property but you can't have a horse on it.
Fourth, decide how much driving you want to do. I live 30 minutes drive from town/work. 45 minutes-1 hour would be a bit much for me every day, but many people will do it to ensure that their property stays rural. If you buy property adjacent to a housing development, and the economy picks up, your property will ultimately become a odor nuisance and the development's owners WILL work to change your zoning. Then, you're back to the big property and no horse problem, again. "Practical Horseman" talked about this recurring problem as far back as the early '90's. Glad I read THAT article, and talked to lots of horse people before I took the plunge.
Fifth, decide if you want to/can afford to build part or all, or if you want to buy developed. I wanted a real house, a barn for forage storage, and some kind of fencing. I GOT:
--6 bedroom house
--4 car garage
--1 barn w/loft storage for ~500 bales (and stairs, instead of a "fireman's ladder" to the loft!) and a 16' x 19' shelter, w/hay manger
-- 4 acres of divided old, but mostly intact cattle fencing--I replaced it in 2008 with pipe fencing
1999 price, $89,999
We are re-roofing the house, garage and barn this Spring, but won't need to do that ~30K job again. We replaced the boiler, buried the power lines, hooked into existing natural gas, and I always have mistint paint around in my tool shed. JUST so you know that repairs can cost you.
I won't tell YOU what is important and what you are willing to not have, but YOU need to figure that out. I've lived in this county since 1982, and I know that although I live in the "town that time forgot", my DD's could move this property in one week after DH and I die. Price and size and equine use have a market in my county. Look at EVERYTHING, and don't be afraid to fire your real estate agent if he/she is wasting your time. 4 of them thought I had a secret stash of 1/2 of $million extra to spend, so they had to go. I called my last agent and told HER about my property bc I had just met the daughter-in-law of the people we bought from, and the place had JUST gone on the market that day. We had the bid on the property held against subsequent bids, and the only holdup was that they wanted about 2 months to move out. NO PROBLEM!
FINALLY, think hard about what you see. Be willing to walk away if it isn't right for you.
I'm so excited for you!! Keep us in the loop. =D