My suggestion would be to borrow, rent, and/or fabricate gear so that you can get a cheap start to see if you really like it. Then follow what I think Gershon said, do at least a couple of short trips. Then I'd strongly suggest a "shakedown" hike of at least 50 miles.

If you still like it at that point, perhaps the best way to learn various skills and info-bits that will help you succeed on a long distance hike is on a long distance hike. In particular, if you start the AT or the PCT about when most folks do, you can easily find yourself hiking in a group and learning from the group.

So, in short, if you really want to hike half of the U.S., I suggest that you ramp up in a way that gives you better odds of success at hiking a long distance, and then hike either the PCT or the AT "with the herd". In some ways the AT is easier to jump into if you have really little experience; for the PCT, you should have some experience in snow at least, depending on the particular year.

I've been doing something similar to what you're talking about, knocking off long trail chunks. The AT and PCT are well documented, clearly marked, sort of "training wheels for long distance hiking" experiences. If you find you like it and/or get addicted to it, there are a lot of trails to hike. I did about 800 miles this year, and plan to hike the rest of the Pacific NW Trail and half of the Florida trail in 2015.

Here's a good list of long distance trails just in the U.S. (and FWIW I've quite enjoyed a couple of relatively long trips in Europe too):
http://en.wikipedia.org/wiki/Long-distance_trails_in_the_United_States

It's fun stuff if you like it. It does not, however, make you particularly tough or smart or better looking --- in fact, you'll most likely be avoided as a smelly homeless person more than once along the way! :-)