For a budget of about $1000, you can get a very nice, full featured suite of hand tools that you can build pretty nice projects with. And this price is for getting premium quality tools brand new. If you've got more time than money, you can get second hand vintage tools from online auctions and real estate sales and refurbish them to work as good as new ones (I wouldn't recommend going this path if you have no prior experience).
By contrast, you'll blow your entire $1000 budget on a table saw and a planer, and you can't even get very good ones for that price.
Word of warning: do not buy new hand tools from the big box hardware store. Either buy vintage ones or premium tools from woodworking speciality stores. Modern, mass produced hand tools (e.g. saws with hardened teeth) aren't very good, they're harder to tune and are not designed to last a lifetime.
Working with hand tools isn't all that much slower than using power tools, unless you'd do something very repetitive where you do the same cuts on a ton of pieces.
I do woodworking using hand tools almost exclusively (I visit a shop once a week, where I have power tools). I find it really enjoyable and relaxing compared to working with power tools with all the noise, the dust and the danger (the power tools at the shop aren't great quality).
I'd recommend the following tools to get started:
* A rip saw and a cross cut saw (or a Japanese Ryoba which has both)
* 4 chisels: 1/4", 1/2", 3/4", 1"
* A #4 smoothing plane (if you have a good workbench or intend to build one)
* OR a low angle block plane (if you don't have a bench)
* Sharpening equipment because tools don't come sharp out of the box
* A saw file if you got a re-sharpenable saw
* Optional: a coping saw or a fret saw, depending on what kind of joinery you're into
The above will cost around $200-300 and is enough to do quite complex projects.