Since you have a sufficiently large pot and burner, a mash/lauter tun (most AG homebrewers use the same vessel for mashing and lautering) is really just about the only other thing you need.
Yes, a 10 gal cooler is good for what you have in mind. There might be some concern about grainbed depth for lower gravity 5 gal batches if you are fly spraging, but if you're batch sparging, this really isn't an issue.
Bottle conditioning: Robust Porter
Drinking: Saison Dupont clone, tripel
Coming soon: Columbus APA, Rich Red ale