1) If you're gonna be replacing the tiles, I'll assume you'll be replacing ALL of them. If this is the case, it doesn't matter where you start the demolition. But, it DOES matter where you begin the install. (Read on ...)
2) There's plenty of 'stuff' on the WEB to help you with this process from selecting the right tiles -to- the finished job. I went to my favorite search engine, AltaVista, and entered in +"ceiling tiles" & +install Then I got TONS of WEB hits. I picked a couple of them and have listed them below. Some of the info is redundant but this way you get multiple perspectives on the same subject. If you do the search, you can peruse the list and see more sites.
3) As for which is the best ceiling tile, you'll have to compare them. It doesn't hurt to go to a Home Center or a Specialty Store and ask questions. The more you ask, the more you learn, and the more you learn, the better off you are.
When I re-did our family room, we had interlocking ceiling tiles that were stapled to the ceiling. My wife and I don't like the 'look' of ceiling tiles. We re-did the whole room in drywall to brighten it up. The room is on the north side of the house which is the darkest side. The original walls were paneling, so combined with the tiles, it looked real dreary and drabby. Drywall give you more flexibility so I mention it as something to think about. Anyway, the only thing I can add from experience is to be sure there are no nails/staples left in the ceiling. Depending on how old your home is may 'force' you into some unlikely decisions. Before you get too far in the demolition, I'd pick a corner and pull off a few tiles to see what's up there before you go crazy. Take off enough to see between a couple of rafters/joists with your head and a flashlight. At some point, when the demolition is done, now is the time to think about putting in additional phone, cable, and electrical outlets, switches, and fans in. Best to ya and hope this helps.