Some things to consider with your mini-lathe purchase:
RPMs, If you are going to mostly be working surfaces which are 1 to 2 inches in diameter, the typical 2500 Max RPM mini-lathes can be good. If you are working larger diameters, you will need a lathe which can turn slower AND have good torque. If you are planning on making 1/8th to 1/4 inch items, you may find that 2500 RPMs may not leave the finish you desire.
Length: or, the dreaded mini-lathe math issue. The Short answer is, for drilling a bore, subtract roughly 8 to 10 inches from the advertise length of the lathe, and that will be the maximum length of part you can work. Many of the length measurements (for lathes) are from the face of the chuck to the tailstock spindle (with the tailstock pulled fully back, and the quill of the tailstock cranked until it is fully back. The quill has to be moved forward about 3/4 to 1 inch to accept a Morris number 2 taper drill bit or chuck. Then you have the length of the drill (or with a chuck, the length of the chuck Plus the length of the drill). For drilling operations, you may discover you can only work a part that is 2 inches long with some of the smaller length lathes. Drilling is often done before machining a more precise bore.
Motor: Short answer, Brushless is preferred over brushed motors for reliability. They typically generate more torque than brushed motors. For a mini-lathe, I like brushless motors with variable speed control. For a big lathe (outside your price range), a robust all metal transmission with an AC motor.
Tool Post: an OXA quick change tool post (QCTP) is preferred. The typical tool posts on mini lathes assume you have a stack of shims handy to set the ideal tool height. Most people starting out don't have a "shim collection" laying around. The QCTP posts don't need shims to set tool height.
Chuck: Larger the better. Not only does it act as a flywheel to keep RPM variations (and vibrations) to a minimum, but the specifications on many of them are a bit misleading. My 4 inch chuck can only open up to grip a part that is about 2 inches in diameter. To hold a larger part, I must swap jaws on my chuck. A 3 inch chuck is very limiting, and is the common size on inexpensive lathes.
Now, the reality check comes due. I think of mini-lathes as a "platform" to build a good lathe. Most common modifications to improve them include:
Headstock bearings: Press out original bearings and replace them with tapered bearings. This also mean you need a shorter keyed spacer between the (thicker) tapered bearings and the spindle gear. (True for Sieg, Grizzly, Little Machine Shop, harbor freight, and some others), not true for all mini-lathes.
Brass Gibs: Yes, you can polish and shape the gibs that come with the lathe to improve them. Or, you can buy precisely made brass Gibs and swap them out (preferred).
Gears: Most inexpensive mini-lathes come with plastic gears. An experienced person, who works to align them, and never stresses them, may get years of satisfaction with them. Most newbies will end up stripping them at the least opportune time. Consider purchasing a Metal Gear Set to reduce frustration.
Tool Post: If it didn't come with a Quick Change Tool Post, consider this as a worthy upgrade to increase ease of use.
Other things needed/desired:
Grinder: Unless you want to buy a new tool when your old one gets dull, consider a grinder with a platen which can be set at an angle. Learn the dark arts of tool grinding. You can certainly go the route of buying cutting tools with replaceable carbide too.
Saw: A small lathe only works with short lengths of stock. You will probably enjoy the first 5 or 6 times you have to hacksaw through 2 inch stock, but after that, it will seem like work. Most steel shop workers will hide, when they see the guy who wants 20 pieces of steel which are 2 to 6 inches long.
Bench: Something really stout. Wood, even thick wood eventually bows and flexes under the weight of even a tiny lathe. This changes the "level" of the lathe over time.
Sweat Equity: Your lathe and table will need leveled. Your lathe will need the Gibs replaced/adjusted. Your lathe will require initial cleaning and then lubrication. It will need periodic cleaning and lubrication. Your headstock may need aligning, your tailstock is almost certain to need aligning.
Other needed goodies: A set of micrometers, a 6 inch digital/dial caliper, an indicator with magnetic base, cutting tools for left hand/right hand/threading/boring, and drills of multiple sizes. A drill chuck with the correct taper for your tail stock. If your tools use carbide replaceable inserts, at least ten spare inserts sitting around. I find a steady rest useful for larger diameter stock (the chucks on mini-lathes don't grip as firmly as bigger lathes). And let's not forget books on machining, to a newbie they are invaluable.
I don't mean to scare you off, but the running joke around here is: "I spent more on my tools, than what my entire lathe cost". Budget accordingly.