I better not use any online wallet services but anyways, one address is good for only a single tx as to what the wimi states. But due to the fact that it will be messy and too many adresses will be created, people just continued on using 1 single address they're very much familiar with instead of changing addresses every use. What blockchain.info does is actually a good thing for you, and yes, you still keep all those addresses anyways if you just take a little trip around the site.
Then Which are the recommended offline wallets.
I have heard a lot about electurm and mycelium.
They are the best offline wallets I got to hear.
Also I was informed that in mycelium wallets we can have custom address.
Like having my name in it or so.
nobody is stopping you from testing all those wallets out.
even if you like you can install a virtual machine such as Oracle's VirtualBox and then install an operating system on that virtual machine and install all the bitcoin wallets on that virtual machine to test them.
install, Electrum, MultiBit, MyCelenium,.... and try out their features and interface and see which one you like more.
for offline wallet the easier solution may be using bitaddresse.org (check spelling before visit the link)