My first suggestion would be to pick up a copy of the Anarchist's tool chest by Chris Schwarz. The book talks about your basic toolkit needed and is also an awesome instructional on how to build your own tool chest, which is a great exercise in hand tool use. Though I chose a wall hanging chest for my first toolchest, it was an incredible exercise in planning, hand planing, sawing, joinery, nailing, glueups, finishing... the list goes on. I love the book because it is incredibly well written and is actually really interesting and engaging, something I can't say for most woodworking books. It talks about bare bones stuff- what you need and what you can forget.
When I first got started I got way too excited about all the fancy gadgets and gizmos and wasted a lot of time and money at the outset on things I didn't need. In my experience, it is way better to invest in high quality tools for your bare bones toolkit and get to practicing instead of wasting a whole bunch of time trying to amass the perfect collection. Something I didn't think about when I was getting started was that most of my woodworker friends and mentors had been doing woodwork for many years- a long time to amass a large collection of tools and amortize out the initial tool investment.
In my experience, you can do pretty much everything you need to with two bevel edge socket chisels, a 1/4" and a 1/2" a number 3 or 4 plane and a number 6 or 7 plane, a dovetail saw and a good rip and crosscut saw. I went the "cheaper" route of restoring antiques, which if you learn how to do well and you don't get distracted by all the shineys (and not so shineys) on eBay and elsewhere, that can really work for you.
That said though, after buying a few duds and not knowing really what I was doing at first, I probably would have done really well to just buy the bare basics from Lee Valley Veritas or Lie Nielsen. They come out of the box ready to do woodwork and you can get started practicing sawcuts and mortises and dovetails right away instead of starting with a huge, messy restoration project that may or may not go as planned (someday remind me to tell you about how I disintegrated a lot of antique calipers in vinegar). They are set up right, and are heirloom quality so they hold their value if you decide handtool woodwork is not for you and you just want to sell them.
That said though, the hunt for good tools in surprising places, relationships along the way and restoring pieces of discarded, rusty history has been just as much if not more thrilling to me than handtool woodwork itself. So if you're like me in that way check out the blog post on restoring old tools for more info on how to do it.
When I first started spending time with Frank, my 93 year old woodworking buddy, I was always confused as to why he always wanted to use power tools and was never interested in handtools. I think a huge part of it is that he has never had the chance to use a truly sharp and well tuned handtool. I restored one of his planes for him and I'm pretty sure it's still in his drawer right where I left it after I gave it back :). And, especially for beginner hand tool users, using a poorly sharpened or just a poor quality handtool can be frustrating enough to turn one off to them forever.
That is why I'll recommend again that beginners just pony up the extra bucks for well tuned handtools at the outset. And one of the most important first things a handtool user needs to learn is how to sharpen tools. I might write an article on how I sharpen if someone requests it, but for every one woodworker, there are ten different ways to sharpen a tool. Do some research, pick one, and stick with it. Otherwise, you're going to waste a ton of money on all kinds of jigs and fixtures you simply don't need.
Once you have a couple sharp tools to work with, GET STARTED! Practice, practice and more practice will get you there. Some people pick things up easier than others, but anyone can do woodwork. Back in the day, I kind of imagine run of the mill furniture builders were the McDonald's employees of today. I practiced dovetails time and again using scraps of cabinet grade plywood because it was already flat to start with and that eliminated one of the possible variables. I didn't have a dovetail marker (still don't... Chris! how bout that trade?), I just measured the angle of the dovetails on my brother in law's tool chest and transferred it over to my workpiece. My biggest struggle at the outset was gripping the saw too tightly which made my cut wander. I'm no handsaw expert, but I think it was Chris Schwartz who wrote that a saw should be held like a baby bird, and ya'll know I have all KINDS of experience holding baby birds. That helped.
When practicing cutting mortises and tenons, again, just go for it! Make sure your wood is square before cutting and you will save yourself lots of headaches. Be mindful of the tolerances of your steel, or your first mortise might become a coffin for half of your chisel like mine did. I would actually recommend drilling out the waste and then cleaning it up with your chisels unless you have a mortise chisel, which is an awesome tool to have, but not a necessity at the outset.
Practice using your handsaws a lot. Not only will your lines get straighter and straighter, add some afternoon hand planing in and you'll never have to go to the gym again! So. Pick up your copy of ATC, read it, grab some tools, and get practicing.