There about 1000 diesel v gasser threads on here, so just a few comments. You can figure out the rest with some reading.
First whoever "enjoys" towing with pretty much any gasser even the mighty 8.1 over a LB7 Dmax or any modern diesel is just trying to justify their purchase......unless they enjoy less power and worse fuel economy apples to apples.
Second, no letting your truck sit for a week or a month at a whack won't hurt it a bit, none of them. Unless you're really going to use it that little, then it's a lot of $ to sit.
Third, yes your use is squarely within the capability of a 3/4ton.
If I had up to $35k to burn on a used truck has or diesel, would be roughly in this order.
Spend $5k more and get a new ram tradesman from one of the high volume dealers. Or another brand of your choice if they are 13-14k off (Used prices are overinflated to the max right now, and pretty much all used diesels suck for what you pay. Most around here are asking new prices for used trucks, lol)
Spend $25-30k on a great, needle in a haystack, grandpa owned southern truck,no rust, low mile, pre 08 Dmax or Cummins (only Cummins with a 6 speed manual trans though)
Spend up to $35k on he lowest mile newest gasser 250/2500 you can find.