Probably the most popular lathe that fits that description is the well known 9x20 that is sold under a bunch of different brand names and different sellers, from the respected Grizzly tools to Harbor Freight. Unfortunately unless you happen onto an old American or European machine (getting harder to find all the time!) you will be stuck with a Chinese import of very poor quality such as that popular 9x20. Some larger Chinese imports are actually decent lathes but there seems to be a definite decrease in quality in anything less than the 12x36 machines and the smaller ones are more suited to softer materials like plastics. DON'T fall for "Brand Name" expecting better quality because most Chinese machines are the same regardless who sells them and a better "Brand" will not mean better quality. An example is that 9x20, The older Jet brand sold for over $1200 while the SAME EXACT machine at Harbor Freight is usually less than $700 and the only difference is the color! The newer Jet looks somewhat different than the others but it is cosmetic and a trick to make you think it is different. Grizzly, Enco and a couple of others have this lathe priced somewhere between HF and Jet.
That 9x20 is of course only one example but it is by far the most popular and I suppose if a person is willing to accept it's limitations it can be usable, I used mine (Jet) for several years but honestly IMO it is a piece of junk. If you have room for a bigger lathe I would strongly recommend at least a 12x36 because there is not that much price difference and the smaller hobby lathes are very limited in usefulness.
What do you intend to use it for and about how big did you have in mind?
Also I would strongly suggest avoiding the 3-in-1 multi-purpose machines because each function is so compromised in the attempt to be able to do everything that it really does nothing very well.