Most of what I see in the 2nd image are broadleaf weeds, like dandelions, thistle and spurge. First picture has most of those, with some plantain thrown in the mix; I'm not so sure about the big clumps of green, unless it's tall fescue clumps. I'd echo what g-man said about the Ortho Weed B Gon. Good thing about this product is that it has quinclorac, 2, 4-D and Dicamba, which will pretty much knock out 85% of the weeds that you have enmasse. Ortho's site says you can spray when the temps are below 90.
With the size of the lot that you're dealing with, I'd go with the hose-end sprayer option. Just hook up your hose, and spray it down. Do it in the morning, while the dew is still on the grass, and before the heat of the day. You'll see dead weeds within a few days. Measure your lot size here.
Pretty easy to do it. As far as fertilizer goes, you can't go wrong with Milorganite. Easy to apply, relatively inexpensive, and safe for all lawns. 1 Bag should do you just fine, for your lot size, I'd say 1/2 of the bag would work.