If you can get your hands on a used real lathe that isn't clapped out then that's the way to go. I live in an area where there wasn't a lot of industrial activity so this wasn't an option for me. So being on a tight budget I started out on a mini-lathe.
The way to look at mini-lathes (or most "budget" Chinese simple manual lathes < $10000) is that they are kits which have been assembled so they fit in a crate. While they do actually operate, they need a lot of hand finishing to work well. Finishing them can be a great educational experience if that is what you're after, but if you just want to turn parts they will be frustrating. I probably spent a good year making stuff for the lathe or modding the lathe rather than making anything useful.
If you have a project in mind, there are couple critical dimensions you'll want to look at. Swing over the cross slide (not just swing, which is kind of useless for anything long) and bed length. Bed length should be at least twice what you plan to work on, since for example if you want to bore a part you'll need n length for the part and another n for the boring bar. Note if the part is particularly long (over 4:1) you'll likely need to support the end with the tailstock which takes more bed length. Weight is also very important as it implies rigidity which is good for precision and/or heavy turning.
If you have a budget in mind, know that you'll spend about half of it on the lathe and then the other half on accessories. A lathe by itself is rather useless; you'll need tool bits, drills, chucks, centres, measuring devices (caliper, feeler gauge & dial gauge is enough but a DTI gets handy especially if you get a 4-jaw, and you'll certainly end up with a mic & snap gauges at some stage), a bench grinder and of course some material to make stuff out of. The more expensive the lathe, the more expensive the stuff you're going to need to go with it.
Anyone selling a machine tool with an aluminium bed is either cruel, or doesn't understand materials. One of the many reasons cast iron is used for machine tools is that it dampens vibrations. Try to make a tuning fork out of cast iron. Then make one out of aluminium. Trust me on this.
The lathe is the ultimate tool though. It's ancient. It's as precise as your skill allows. It can really make just about anything on it; not just round things. You are no longer at the mercy of what's available to you at the moment. Just tonight I needed a 1.5" pipe thread nut that none of the hardware stores I visited had anything like. No problem, I just made my own.