I started out with a 5 gal cooler, false bottom etc... but would really recommend something in the 7 - 10 gallon range. Here's a great post about different size mash tuns
. As for maintaining temps. I injected spray foam into the lid and with a 5 gal. cooler, the head space is very low so I had no temp fluctuation for my mash. Oh, and pre-heating your MLT is a good idea if you're strike water is at or near your mash temp.