What size batches do you think you'll be brewing?
Igloo 10 gallon round coolers run around $32-39 when I got them at Home Depot a few years ago.
I agree that they're well insulated, especially the lid.
Buy the SS weldless bulkhead/spigots from your LHBS or online.
Cooler conversions are so ridiculously easy.
The Bazooka braid screen works well for 5 gallon batches.
However, if you're considering 10 gallon batches or high gravity beers or wheat/rye beers, I would recommend you consider using a rectangular 82 Qt (20.5 gallon) cooler as it will make stirring, water/grain ratios, step infusions, and lautering so much easier to achieve with the extra capacity (and less mess). Also, from personal experience, you want to avoid grain bed compaction which occurs whenever the height begins to exceed the width of the grainbed. An Igloo cooler is around 12 inches wide and 24 inches tall inside.
Again, I've had a lot of frustration using the 10 gallon round cooler for 10 gallon batches, high gravity and/or wheat beers--So, if you intend to do those, I would kindly suggest you use the 10 gallon round cooler for a HLT and use a larger rectangular cooler for the MLT.
If you haven't already, be sure to check out Denny's website on how to build a great mashtun. Classic and effectively simple (and I mean that in a good way). Easy to set up, use, clean, and put away.