You are correct that certifications are "lifetime" and pretty worldwide - the two most common agencies are PADI and NAUI. PADI seems more common in the U.S., but both are accepted everywhere. There are a couple of other certifying agencies, but those are the two main ones. Even though it is "lifetime", many operators will encourage you to get a refresher course if you dive after a year of inactivity.
Most places will want you to get your own mask, snorkel and fins for your certification process - and you'll use their BC, regulators, tanks, computers/gauges, etc.
I've found that what you start out with is not that important (in terms of mask, snorkel, fins) since you'll likely upgrade at some point soon anyway. I actually use a pretty cheap mask and snorkel myself (and am happy with it) - but have upgrade fins several times. I started with full-foot fins, and very quickly abandoned them.
In terms of buying your own BC, regulator, gauges & computers, etc - I'd recommend renting for a while (lot of dive destinations have really good rental gear these days), and THEN deciding what you want. I'd also suggest mixing and matching - because some companies make great BC, some make great regulators, and some make great computers. DO NOT let some dive shop push a package deal on you, just because that is the brand they use.
Once you want to buy gear, definitely check out scubadiving.com (their magazine is also really good to subscribe to, so I'd recommend that) - they do a LOT of gear reviews, and you cannot go wrong with buying a "Best Buy" and "Tester's Choice" piece of gear.
In terms of diving in land-locked states (I live in MO and my wife in TN), we really don't do any local diving at all.
The occasional quarry, or lake or flooded mine or whatever just doesn't interest us, so unfortunately the only time we get to dive is when we travel. However, some people might really enjoy that kind of local diving, so you should definitely try it, even if you end up only diving once or twice a year when you travel to do so. Sometimes, you can find really good deals on 5-day trips of Cozumel or Bonaire or things like that, so travelling to dive doesn't have to be ridiculously expensive.