Not sure about you getting tickets, it all depends on what match you want to go to. If it's a big game, then they'll go to members first, if it's a smaller game then you'd be able to get them through the club directly is they go on general sale.
As for where you want to sit....well, the Matthew Harding end is certainly the most lively but it's mainly filled with regulars so doubt you'd get anything in general sale in there.
I've been quite lucky to get tickets in the West Lower and the views are good, just not much atmosphere. I know a couple from the US who traveled to London and took in a CL game against Genk, and they got tickets in the east Lower.
As for a beer or something before hand, Parson's green is a good area with a few bars, but it's a bit of a walk to the ground. Or you just get off at Fulham Broadway and there are a few decent bars around there. Not sure what's all being used for home support theses days, but there was the Slug and Lettuce.
Oh and welcome to the boards. Chicago is a fun town...i'll be there again in May.