Welcome!
Once you have a lathe, a whole new world (only one?) opens up for you.
Remember that you can do small work on a big lathe, but not the other way round.
A good British lathe may be within your budget, but if ex Industry may have been driven to death. Ex School / Tech College machines may be relatively unworn, but scarred from careless use.
The later Asian machines can be of quite reasonable quality (Hardened beds etc, and quite rigid).
If you are not sure about a possible machine: You will get a lot of first hand knowledge on here, but when going to look at a possible purchase, do take someone knowledgeable with you to examine and try out the machine.
(Which it is a good idea to give an indication of your whereabouts)
This Forum will provide lots of hints, tips, and advice on tooling, techniques and accessories.
Soon, you will be able to really enjoy restoring your landies!
Howard