I'm assuming you're looking for the US standard small size, 6-3/4. The previous best was rag content envelopes, now called cotton fiber. Unfortunately, they don't exist except in oddball stationery sizes these days. And those are expensive today, like 40c-50c an envelope. The best you might be able to do nowadays is an envelope in a somewhat heavyweight stock like 24 lb. The office supply stores probably won't have anything like that, you need to go to a real stationery store or online envelope supplier. I would not use self-stick/self-adhesive envelopes since there's nothing archival about that stuff for envelopes.
I used to use Avery peelables long ago when I was sending away for special event/pictorial cancels. Results would vary, since there is no accounting for mail sitting in a hot mailbox or postal vehicle, for example. Pencil addressing is tedious but it works. Use an HB pencil, so you can erase all with a soft eraser like a Mars Staedtler. Then again, the cancel may cover the address, but so can it cover an address label.
Do you get your covers sent back under self-addressed return cover? It's recommended, because covers sent through the mails may be easier and preferable, but are overcancelled at least a third of the time nowadays.