It depends on why you want to play a remake. If you're looking for a nostalgia trip, then I'd start with the remake of whichever games were your favorites. If you want a remake with the most content, I'd go with HG/SS, for the reasons mentioned by previous posters. And if you want a game with all of the modern improvements that just happens to be a remake, go with OR/AS.
HG/SS are my favorite remakes. They definitely offer the most content, especially post-game content, of the remake options, and they're playable on the newest system or any other member of the DS family (unlike FR/LG). While the lack of wifi features is disappointing, they're still great games, and even with just a single system, you can enjoy most of what they have to offer. (Add in an extra DS, and you can trade with yourself, further reducing the disadvantages of not having wifi.) They also do a great job of staying true to the original games while adding in new features (like the Battle Frontier and Pokeathlon). Admittedly, gen 2 was my personal favorite, so my nostalgia goggles bias me towards HG/SS over the other remakes, but I think they're objectively the most fleshed-out remakes available, if you can get your hands on them.
OR/AS, the gen 3 remakes, offer the newest features, but as others have said, they felt a little bare-bones to me. Yes, they improved the graphics, have great breeding mechanics, etc., but the post-game is lacking, and they don't have features like the Battle Frontier. If you're a gen III fan, then I suspect you'll still love them, and some of my negativity may stem from the fact that I didn't like Hoenn that much in R/S. (That's not to say OR/AS aren't good--I enjoyed them a lot--but they weren't of the same quality as HG/SS IMO.) Since OR/AS so easy to find these days, you may as well pick them up and play them, but if you want a remake that's packed with content and you're only able/willing to get one, I would go with HG/SS.
I enjoyed FR/LG, but they're pretty dated at this point, and they can't be played on the newest system, if that's an issue for you. If gen 1 was your favorite, I would still try to find them and play them. They stay very true to the original games, though there isn't too much expansion in content (there are a few islands, a couple of side-quests, and a second-round Elite Four, as well as breeding and the like, but that's about it). They are pre-physical/special split, which seems to bother a lot of people, so be aware of that if that matters to you.