Phoenix Wright
Legend
Loyaler
If you are asking about the best hands for these games, then I assume you already loosely know the rules/formats of the games (and if not, then I'm sure CardsChat forum threads on that topic exist somewhere). Take my words lightly though; I strictly play NLH except like once or twice I played some other forms of poker (like Omaha, Razz etc.) for play-chips. Obviously, whatever I say, I barely know No Limit Holdem (only learned the rules about a year ago) and I know even less for Omaha 
In Holdem, the best possible hand preflop is AA (pocket Aces, pocket rockets, bullets, or whatever you might call them). Even the best preflop hand of AA is beatable though; against a random hand, AA wins about 85% of the time. This wins a ton (as the best possible starting hand should), but those 15% times you lose will surely come here or there.
In holdem, some of the best hands preflop would be the high pocket pairs (how high depends on who you ask and how nitty or aggressive they are) like say QQ, KK, AA. Another potentially powerful hand is AK. Ace-King suited or offsuit is a potentially monstrous hand. If you connect with the flop, then you are probably ahead already with top pair and top kicker. Even when your AK doesn't connect by the showdown, the high cards might still be enough to win if the opponent missed a draw or something like that. However, as you may have guessed, you don't want to be blasting away with AK and only have Ace-high by showdown; this hand is potentially very strong, but can be tough to play by many.
In holdem, only playing the cards I mentioned would be too nitty of course, but you only asked for the "best starting hands." Generally speaking, pairs like 99+, suited broadway cards (like KQs), and even some Ax hands (Ace and something else) might be solid and playable based on the situation, seat at table, effective stacks and so on.
Omaha is much trickier and I know even less about. However, here are some of the best hands in Omaha (naturally, even the pros debate which hands are better than others at times).
The best possible starting hand in Omaha is AAKK double suited (like Ad-As-Kd-Ks). With this hand, you have a lot of potential for strong flops. You can flop three of a kind, two different Ace-high flushes, a straight and so on.
Unlike NLH where everyone agrees AA is probably the best hand and KK is second best, the second best starting hand (and the rest) is more debated in Omaha. According to T.J. Cloutier, he likes AAJT double suited. Also high in preflop value is any AAxx hand, but these hands might lose a ton of value in multiway pots.
Pretty much, Omaha has so many "high" hands made, so you want AA-and a big pair (like AAKK, AAQQ, AAJJ) or AAxx hands. After this is basically just broadway cards with pairs in them already (like KKAQ, KKQJ).
What you want to stay away from in Omaha are hands that look enticing, but are really low cards since so many "big hands" are in Omaha. A hand like four connecting cards are really dangerous if not just trouble; if you aren't playing some High-low Split variation of Omaha (different game and strategy), then these low cards are likely to lose to higher straights/flushes even if they do hit.
Good luck with these very different card games
In Holdem, the best possible hand preflop is AA (pocket Aces, pocket rockets, bullets, or whatever you might call them). Even the best preflop hand of AA is beatable though; against a random hand, AA wins about 85% of the time. This wins a ton (as the best possible starting hand should), but those 15% times you lose will surely come here or there.
In holdem, some of the best hands preflop would be the high pocket pairs (how high depends on who you ask and how nitty or aggressive they are) like say QQ, KK, AA. Another potentially powerful hand is AK. Ace-King suited or offsuit is a potentially monstrous hand. If you connect with the flop, then you are probably ahead already with top pair and top kicker. Even when your AK doesn't connect by the showdown, the high cards might still be enough to win if the opponent missed a draw or something like that. However, as you may have guessed, you don't want to be blasting away with AK and only have Ace-high by showdown; this hand is potentially very strong, but can be tough to play by many.
In holdem, only playing the cards I mentioned would be too nitty of course, but you only asked for the "best starting hands." Generally speaking, pairs like 99+, suited broadway cards (like KQs), and even some Ax hands (Ace and something else) might be solid and playable based on the situation, seat at table, effective stacks and so on.
Omaha is much trickier and I know even less about. However, here are some of the best hands in Omaha (naturally, even the pros debate which hands are better than others at times).
The best possible starting hand in Omaha is AAKK double suited (like Ad-As-Kd-Ks). With this hand, you have a lot of potential for strong flops. You can flop three of a kind, two different Ace-high flushes, a straight and so on.
Unlike NLH where everyone agrees AA is probably the best hand and KK is second best, the second best starting hand (and the rest) is more debated in Omaha. According to T.J. Cloutier, he likes AAJT double suited. Also high in preflop value is any AAxx hand, but these hands might lose a ton of value in multiway pots.
Pretty much, Omaha has so many "high" hands made, so you want AA-and a big pair (like AAKK, AAQQ, AAJJ) or AAxx hands. After this is basically just broadway cards with pairs in them already (like KKAQ, KKQJ).
What you want to stay away from in Omaha are hands that look enticing, but are really low cards since so many "big hands" are in Omaha. A hand like four connecting cards are really dangerous if not just trouble; if you aren't playing some High-low Split variation of Omaha (different game and strategy), then these low cards are likely to lose to higher straights/flushes even if they do hit.
Good luck with these very different card games