dv, you'll have to cover all three bases out of DCA - DCA, IAD and BWI. Well, now that I think about it, I'm not sure if BWI has 737s or airbuses going there, so you may not need to cover that one. Although IAD is going to be the primary you fly in/out of.
Both ORD/MDW and IAD/DCA will have a decent number of flights. You'll not want to limit yourself to UAL jumpseat; I've jumped more on offline carriers than online.
Pick an airport that you'd prefer to fly out of - FLL or PBI. You may need to test each airport for a while, but I'd bet that FLL will be your first choice since you'll have multiple carriers out of there.
Then you're going to want to check on availability to ORD/MDW and IAD/DCA. For MDW, it's just an L (their mass transit) train ride to ORD, with one connection. For DCA, you can take the Metro to West Falls Church station and then catch the Washington Flyer (they give an airline discount; show your ID). For BWI, I've rented one way from Avis for ~$25. I'm sure that there's cheaper transportation, but I haven't figured it out.
I don't know which carriers serve FLL and PBI; I imagine JetBlue (direct IAD), USAirways (direct DCA), Southwest (direct BWI), along with several other carriers - either direct or with stops. You might also want to check on carriers such as Apple Vacations and other package carriers which may serve Chicago/DC direct.
I really don't think that it's going to matter if you go with ORD or DCA; both commutes are doable. I discount the comments about MIA hub closing; that's been closed for years and I'm sure that more than a couple of the pilots from that hub are now based out of ORD.
I think that you'll figure in pretty short order which hub you'd prefer to commute to.
Out of all of your choices, I'd rank ORD/DCA as 1/2 (your choice), then DEN, then LAX, then SFO. That's my best estimates of pain involved with a commute.
Unless you're firmly rooted in the MIA area, you may want to move to improve your QOL.