Woodworking with nothing but hand tools vs woodworking with power tools is kindve like cooking over a campfire vs using a gas range; both will do the job, and both require skill, but one is easier to get started in. Hand tools still have their place, but I wouldnt want to build a book shelf with nothing but a hand saw and a screwdriver.
If you're just starting off, look for a decent table saw, as someone already mentioned. A used model will do you fine, something like the older craftsman contractor saws. If you're not opposed to spending to get a new saw, Lowes carries a delta brand contractor saw, fantastic bit of machinery. A table saw will do nearly anything you could want when it comes to wood working, and is a lot more enjoyable than using hand tools to boot.
Again, there's nothing wrong with starting with hand tools, but it really isn't they way I'd want to learn. Its a lot easy learning something when instead of having to juggle design, layout, tool holding technique, cutting technique, and the like, you can boil it all down to "make sure everything is laid out properly and push".