Peter, welcome to the site! I've been using Okuma Reels for several years & like them very much. Not expensive, good quality for the price & have held up very well. I have a couple of Sierra's & Integrity's. I rarely fish for trout, so the Sierra's get used for panfish on 3 & 4 wt rods, while the Integrity's get used for LM bass, SM bass & Striped bass on 8, 9 & 10 wt rods.
On my 6 wt is a Lamson LP-2 reel that I bought in 1989. This was before they became Waterworks/Lamson. It's no longer made & is still going strong. Lamson reels are generally more expensive than the $100 limit you've set, but if you can find one for that price or under, they're a fine, well made reel.
I use 3 in 1 oil on my fly reels. You really don't need a special oil, and any light reel oil will work. With hard use, I'll clean & oil them 2 or 3 times a year unless they get dunked, then I'll do it more often. I also fish in brackish water quite a bit, so have to be concerned with salt. Have never had a problem with any fly reel in the 47 years I've been fly fishing.