A lot of people seem to be suggesting online wallets (blockchain.info, coinbase).
Granted, these wallets are very appealing for a new user because the learning curve is small, they're accessible on every place where you can have access to the internet and they might have neat features like paying your fee...
However, OP, be carefull: if you read this forum, you'll see a lot of horror stories with these online wallets... They go bankrupt, your funds gets stolen, they lock your account,... This is the price for a smaller learning curve, easy access and reduced fees. Don't be alarmed tough: most users are satisfied with these online wallets, most people don't have any issues with them... But the ones that have issues with online wallets are often left hanging (you need thirth party support to solve your problems for you)
If you want to learn how to use bitcoin in a proper way, i'd suggest starting with a desktop wallet. Bitcoin core is the standard one, but it might take a really long time to sync (it basically needs to download and verify all the blocks which contain every transaction ever made with bitcoin). A good newbie alternative are SPV clients like electrum or multibit HD. I'm a big fan of electrum, it's pretty newbie friendly, but still has a lot of coin controll features once you learn a thing or two about bitcoin...
Just my 2 satoshi's on the subject