On my old stove I could boil 5 gallon batches by straddling two burners. My new stove is big enough to boil a 5 gallon batch on the biggest single burner. It looks like the burner I use to brew on is 14,000 BTU, although my stove also has a 17,000 BTU center grill burner too.
As far as the kettle is concerned, you can use either aluminum or Stainless, but I recommend stainless if you can afford it. 10 gallons is a nice size for 5 gallon batches, but you could go as low as 7.5 gallons if you are careful. I usually use a 7.5 gallon aluminum turkey fryer kettle when I am brewing in the kitchen. Stainless is less likely to react with chemical used in cleaning and is much less likely to dent or scratch than Aluminum, but Aluminum works fine and is lighter. If you go with Aluminum the experts suggest boiling water in it first to create an oxide layer on the inside.