My 1st and strongest suggest to you is to buy a car that has suspension. I prefer a swingarm car but a traditional 4-link works good as well. Hardtail or slip joint cars are not for the inexperienced driver. They can become a handful very quickly when trying to get them stopped or on a rough track.
As for what to buy, well I would tell you Racetech gets my vote but there are a lot of good cars out there. Undercover, Worthy, Mullis, Danny Nelson and Miller would be some of my top choices. With the budget you have in mind the car will end up being a little older. The 1st thing to do is make sure that the driver is comfortable in the car meaning the fit is good and she can reach all the switches on the dash without issues. Next exam the frame. Make the owner remove the body panels. Look for signs of stressed or cracked upright bars in the front, behind the driver and in the engine area. Make sure the car has a recent certification. Do not buy a car without a current tag that you are told will certify. There is most likely a reason there is not a cert on it now. Take a look in the trailer or for signs of a round rubber air bladder. The air bladder goes under the car when tied down and inflated to help stop the chassis from flexing during transport.
My final suggest, find a fellow racer that is at your home track that has experience with dragsters. Take time to talk to them and get as much time in the lanes looking at different brand cars. You may find your best deal is not advertised and sitting at your home track.
Good luck