Go with something light. A cream ale or a light pale ale. Ferment for 10 days to 2 weeks and bottle condition for 3 weeks. You will have to get it going ASAP.
+1 on this, though a cream ale is difficult to do properly with just extract. A Mild or a lighter Brown Ale might also be a good choice.
Here is a partial-mash version of the recipe I mean to brew tomorrow, which I expect to be ready around that same time period:
Newton Pulsifer London Brown Ale (final partial-mash recipe)
2.25 lb. Amber DME
1 lb. Maris Otter pale malt
1 lb. 45L crystal malt
1 lb. Victory malt
8 oz. Special B
8 oz. Chocolate malt
1 oz. Fuggles hop pellets (4.8%AA), 60 min.
Ringwood Ale yeast (Wyeast #1187)
I will be making a 1L starter for it, which should make the whole process go a bit faster. Another recipe you could try would be a simple best bitter like this:
Supergrass Best Bitter
5 lbs. Amber DME
or 8.5 lbs Maris Otter pale malt
1oz. Fuggles (4.8%AA), First wort hopping
1oz. Fuggles (4.8%AA), 60 min.
1oz Fuggles (4.8%AA), dry hopping 7 days
Burton Ale Yeast (White Labs #023)
Despite the name, I promise it won't snitch on you
Again, a 1L starter would speed things up by at least a few days. If you do the extract version, add the first wort hops to the kettle as the water is heating to boil; it wouldn't be as effective as it would be with an AG wort where the malt is already in solution, but it should still work.
