I have a 10 gal round cooler i made into a mash tun. (plenty of online tutorials on that). don't bother getting a 5 gal, you'll just kick yourself and get the 10 gal later anyway. (my 5 gal is sitting in the garage, unused).
I have a 5 gal and an 8 gal kettle. I brew right on the stove top, so no propane burner needed. I may get one down the road if i move my operations outside; but in florida, i much prefer brewing indoors. If i were to change anything right now, it would be to get a 10 gal kettle instead of the 8 gal. With both kettles, i am easily able to heat my water for mashing and start my boil with the first runs from the mash.
i agree, chiller is needed. especailly if you have a large kettle that won't fit in the sink with ice.
Tap 1 - DanDan the Elder DIPA (Sorta Pliny Clone)
Tap 2 - Rye Rhapsody Bohemian Pilsner
Tap 3 - Irish Red (Fermenting)
Tap 4 - Raisin Brown Ale
On Deck - Some other DIPA
In Bottles: Maple Barleywine, Peanut Butter Porter, Strawberry Ginger Cream Ale, Sweet Ruination IPA