1.e4 Nf6 2.e5 Nd5 3.c4 Nb6 4.c5 Nd5 is known as the Chase Variation and is playable, though not considered to be particularly great for White.
At the highest levels, the most popular variation for White is the Modern Variation, 1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.Nf3. However, Black is left with a lot of freedom about how to continue, so White needs to be ready to handle a lot of continuations.
At club level the most common continuation seems to be the Exchange Variation, 1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.c4 Nb6 5.exd6 (note that moves 3 and 4 are often reversed). Play proceeds differently depending on how Black recaptures the pawn.
The most aggressive (and most principled) choice for White is the Four Pawns Attack, 1.e4 Nf6 2.e5 Nd5 3.d4 d6 4.c4 Nb6 5.f4. White stakes out a ton of space but has to prove that he hasn't become overextended. Play often becomes very tactical.