If this is your first venture in IL then you should buy locally. Buds does have top notch prices and service but shipping it to the local FFL is where the roadblocks can pop up. YOu got a lot of good advice here but being that Chicago just changed their laws (barely changed) then using your local resources is the way to go.
Rinks has good prices for something they have in stock. Their transfer fees are outrageous. They are telling you (without saying it) that they will sell you their gun for a good price but a gun from any where else.... forget it. They also have good prices on used/consignment guns but a poor selection.
Mega sports carries almost every gun presently made. They are displayed beautifully and you can drool all day. You can hold them and see if you like the feel, balance, trigger reach, etc but their prices are higher than Gander Mountain.
They do offer a nice selection of rental guns but their range fees are high and you have to use their targets. It is modern state-of-the-art equiptment, though, where rinks is old school, dark lanes that has no heat or A/C. You can shoot, though, at a very reasonable price at Rinks.
Gander Mountain does have a nice selection but unless they are on sale they are really high. They are also under-staffed so unless you plan to buy that day you won't get much help with talking to someone and playing with the pistols.
Go the route of buying from a local shop to start with. They will make sure you leave there legal and compliant with local laws. If you haven't gotten all of your permits in order no shop will sell or transfer a gun to you. Their job is to make sure you can legally own the gun so if you are cutting corners you won't get what you want.