No need for apologies. Your thread is valid - just takes some understanding both ways for what you are looking for vs. what is available. It's a bit like someone saying they are thinking of buying a new car and asking what they should buy - it is difficult to recommend something when you don't know the priorities & needs for the purchases - commuting/sport/off-road/kids, gas/diesel/electric, fuel efficiency/load carrying capability/high performance, car/SUV/Truck/hatchback, etc. So please stick with it here, you should get some good advice as members understand more your needs.
For your preferred budget you should be able to get a good EL84/6BQ5/7189 or 6V6 integrated amp. These are typically in the 5-18W+ range depending on configuration & design e.g. single-ended, push-pull, parallel push pull etc.. Vintage can be a good option if updated to spec as many have excellent designs & components. Modern amp options can provide creature comforts such as remotes and easy bias set (for fixed bias amps). There are dozens of options here and every member will have their own favorite. Most well recognized brands & models will sound good, so doing a little searching for reviews (lots of threads here & elsewhere) will help.
If you move up to the 20-35W range with 7868, 7591, 6L6, EL34 type tubes, e.g. as suggested by primosounds, you will likely move into the next level above your preferred budget. The Dynakits or vintage Dynaco ST70 amps are a popular choice; the ST70 is a ~35W power amp with EL34 tubes, optionally 6L6 tubes. In this bracket you can also find items such as Fisher, H. H. Scott, Sherwood, Pilot, HK, Heathkit, Sansui and many other integrated amps or receivers in vintage. All of these choices generally provide excellent performance and most vintage have appreciated in value of late. Modern options may or may not hold value as well depending on make, performance reputation, manufacturer recognition but there are some excellent modern amps out there.
Then we can move up in power & price - or in prestige & price, perhaps to McIntosh, Luxman, Manley Labs, Leben - many variables but as a first amp I would suggest keep it simple before getting into big $.