You are in luck with stating in your location in the avatar that you are 15 minutes away from the Castle. That means one of 2 things, you are in Florida or you are in California.
You'd be hard pressed to find a $1000 car up here in the north that wasn't a rusted out ready for the junkyard car. I just sold my Honda Civic with 187,000 miles on it for $300. I just put a new head gasket in it and it ran fantastic. But it was ready for some more extensive bodywork for the 2nd time. There comes a point where it's not worth fixing the rust anymore and it begins to happen at 150,000 miles and surely happens when you reach up to 180,000 +.
Rust free Honda Civics with close to 150-200,000 miles should be easily in your price range. They run forever, it's the rust that's usually the problem up here in the salty winters. Even if you need to fix stuff, parts are cheap if you do the work yourself. My $900 quote from the shop replacing the head gasket and timing belt turned out to $29 for the head gasket and $19 for the timing belt parts and I did it myself over a weekend (could have been just 1 day but it was too HOT and humid out for me.) Saved myself over $800.
If you can still find them, late 80's and early 90's Toyota 4x4 4 cylinders are another bullet proof vehicle. They also will run forever. The only reason I got rid of mine was 1 was totaled and the other rusted out. Again, it's the salted roads in the winter problem. In fact, my 88 4Runner was totaled twice and I put it back together with junkyard parts both times from accidents with deer. I didn't have insurance on that vehicle itself (the 89 truck was totaled in an road accident and was insured.) Ran the 88 up to 189,000 miles before I got tired of fixing the winter corrosion every year on the rear fenders.
In fact, aside from regular wear items such as brakes and exhaust, in the near 500,000 miles I had on 4 Toyota trucks and 4Runners, I had only ever rebuilt a clutch slave cyclinder on my 88 4Runner. That was the only repair ever done on any of them. And believe me, I did NOT baby those vehicles. They were driven HARD both on the street and off-road.
One thing about the old Toyota trucks, regular maintenance items are done like clockwork. Front brake pads replace at 50k miles. Rear drum pads replace at 150k. Clutch needs done at 150k. They are very easy to work on and you can nearly set a clock to the maintenance intervals.
Just as a comparison to maintenance between an American manufacturer and a Japanese manufacturer, Both my Ford and my Nissan needed new rotors. My Nissan sat there at 165,000 miles on the original rotors and I figured I would finally replace them. The Ford sat next to it in the driveway with 36,000 miles and it needed rotors replaced because it failed inspection. I did the 165k Nissan because I figured I should, it still would have passed inspection and the Ford failed on all 4 rotors at 36k. If you want something you don't need to constantly put money into, look for a Japanese vehicle. It makes a big difference. I have more money wrapped up in my Ford that now has 60,000 miles than I had combined in my previous 5 Japanese vehicles with a combined total of 657,000 miles. I was stupid and bought a brand new Ford instead of a used Japanese vehicle for the wife.
There is nothing wrong with it.. wait there is.. we broke off a clip from the door and we have to replace that.. it was .78 
