I'm currently helping my retired brother in law build a small basement shop where he can do some more advanced gunsmithing, Up until now he's worked with basic hand tools. So the machine tool choices are based on what kind of things he wants to do, and make.
Don't underestimate the value of learning to make things by hand. Becoming proficient with simple tools like files, and hacksaws and a bench vice will give you a better understanding of what you can expect your machine tools to do. I'm not saying you need to spend months whittling a 2 inch steel cube into a 1 inch cube just to prove you can, But I'd try and identify some simpler projects you'd like to make that don't require a large investment. The first machine I would buy would be a decent bench grinder, you'll need to learn to sharpen drills which you'll be using on your Next machine... a drill press. And of course it goes without saying that you will need drills and a drill index. They sell ones that combine fractional/number/letter drills all in one, but I'm not a fan. Start with a fractional set then a number set, and time will tell if you need a set of letter drills. You might think the drill press to be redundant if you are eventually getting a mill of some sort, but I don't think so. Many times in my real job I will use a bridgeport to locate, and spot drill a series of holes, and then move to a drill press to finish the job because it's just quicker and easier that way.
You'll also need a few precision measuring tools. First (after a tape measure which I'm sure you already own) would be a 6 inch scale. With some practice you'll find that it's not too hard to work to .010" with a scale, and many times thats as close as you need to be. You can find various markings, but I prefer a "3R" scale. it gives you fractions on one side and decimal on the other. Even though I tend to be a cheapskate on some things I'd recommend you spend real money on a 6" combination square... 2 reasons) a cheap square that isn't, is worthless, and it's not a tool that's easily damaged or broken. The first one you buy should last you the rest of your life. You'll also probably want a 0-1" Micrometer, and 6" dial calipers. I'd go cheap on your first micrometer, look for a used Brown + Sharp or Mittutoyo on craigslist. And avoid the urge to buy "digital" calipers, Actually I'd say start with vernier calipers, but that's just crazy talk. You'll probably wreck your first set of calipers so I wouldn't spend much money there either.
Now I'm finally going to answer your first question, If you buy the combo lathe/mill machine you will always be faced with tearing down the lathe setup in order to mount a vice to what Is a rather small table in order to do any milling. I think that would be the biggest drawback for me. On the plus side, because a lot of people have bought them and found them to be inadequate, you can usually find a used one on craigslist at a reasonable price. So go ahead and get one if you like the idea, just try and not spend any more money than you have to. See if you can find a toolmaker/machinist who lives near you that would help you check out a used machine, to make sure it does all the things it's supposed to. If you live in the St Louis area I'd be happy to spend half a day helping someone just getting started.
Levi