depending on your credit history and worthiness, it may not be a good idea to apply for three brand new credit cards so you can juggle different reward cards. if it won't hurt your credit and you won't be applying for any large loan soon, than you can try the separate CC route, provided you can properly juggle the different transactions.
I recommend finding a one size fit all card, the Blue Cash back card from amex is actually a decent fit for you (w/ the new, simpler tier rate), as after about 4 months, you'll hit the 5% category for gas and groceries (thats $40 back each month for you) and another $13 for other charges (so $53 total each month, after you break the $6,500 in spending tier limit). finally, the card has no limits on cashback.
check the thread at fatwallet for a list of rewards/cashback cards (split into different spending categories):http://www.fatwallet.com/forums/finance/711457/
I have two chase freedom card that I juggle, although I think I may convert my blue from amex to blue cash and just use that solely as my cashback card.
finally, a few tidbits on using reward/cashback cards:
1. reward/cash back CCs will usually have much higher APR than ones w/o
2. if you don't pay off you bill fully, any reward/cash back you've accumulated will quickly be a moot point
3. many cards have limits on their rewards, especially their higher % back bonuses (like those 5% backs). check carefully.
hope this helps some. if you need more info, leave a response here, PM me, or try sending a note to cap at stopbuyingcrap dot com