If you aren't planning to troll with it, don't bother with a mooching reel, the "center pin reel" you referenced. I've done it in a pinch, it's very annoying. If you are going to be jigging for both bottom fish and salmon, a small reel like this is going to serve you well:
The Tesoro is a 2018 model reel, first shown at ICAST July 2017. The new star drag reels got a lot of attention from anglers, with the improvement in casting of leverdrags it seems there’s a preponderance of lever’s and less star drag reel options for serious anglers who are looking for a high...
charkbait.com
Go for a small light reel of that style, lever drag or star drag, doesn't matter, with 15-20lbs of drag. You don't need that much drag, but by getting a reel with that much, you will automatically avoid most of the junk that's not worth buying. A small reel with lots of drag will typically be well built. I have a couple of the smallest Tesoro reels (5NS), they're great. I use them for ling cod, halibut and jigging for salmon. They are more than strong enough for any fish around here. Light reels are nice, less tiring jigging.
You should be able to get a good, middle of the pack quality wise rod for under $200. Personally, I also prefer light rods. It does depend on what kind of lures you want to use. If you want to use big heavy jigs like these you will want a bit of a heavier rod:
A rod well suited to those weight of jig will be a bit too heavy to reasonably fish smaller jigs you would use for salmon. The rod tip won't bend and flick the jig much, which both feels weird and negatively impacts how the jig will attract fish. I would look for a rod that's suitable for about a 7oz lure max as a compromise between salmon and bottom fish. That should provide a reasonable balance between lures suitable for big bottom fish but still be able to reasonably fish for salmon. Give consideration to slow pitch jigging rods. They will seem unreasonably light, but if you watch a couple youtube videos about how to use them, they're more than strong enough to catch any fish we have. I use the same slow pitch rods for jigging coho and halibut. They work great for both.