You DO NOT want a pot with a built in thermometer. The thermowell sticks out right where the BIAB bag sits, and you'll accidentally rip the bag. Skip any pot with a thermometer/thermowell if you are doing BIAB!! Get a cheap digital thermometer and take your readings from the surface of the wort. Digital thermometers are typically much more accurate. Here's the one I have, which was $19.00 shipped:
I do BIAB, and have the Bayou Classic 44QT (11 gallons) with the optional perferated basket. The perferated basket is PRICELESS when it comes to pulling out the bag and letting it drip over another pot or bucket.
The company that makes these pots is called Barbour International. IF you find the pot under the manufacturer's name, they are about 10% cheaper, and the exact same thing. I got mine with the basket for $92 shipped.
These don't come with a ball valve, but I drilled my own weldless valve and added a dip tube, all from Bargain Fittings. I'm not particularly handy with a drill, and found drilling the proper hole very easy...took me about 15 minutes. The weldless fitting, 2 piece ball valve, and dip tube, along with a step bit for the drill, ran me about $32.00 + shipping (about $38 total).
As far as burners, you are on the right track. The KAB4 is the cheapest model that has the Banjo Burner, which is the same oriface found in the Blichmann burner, and is pretty much the most efficient oriface out there for brewing. Ignore the BTU ratings, most of those guys that put out 100,000+ BTUs heat more air than wort. The Banjo Burner in the KAB4 is about as efficient as it gets for propane. If you are trying to keep it cheap, go with the KAB4. If you have some more $$$ to spend here, you can upgrade to a better housing, but stick with that Banjo Burner oriface. Bayou Classic makes about 12 housing options with that same oriface, then there's always the Blichmann burner