3600 is a solid choice. And should be for quite a while, unless CPU needs change drastically. You can even do high FPS if you want. Future-proofing aside that is one of the best buys for perf/value right now and a damned respectable chip. Definitely go for that first. Between that and the DDR4, you're looking much more ready for modern games and tasks than that FX/DDR3 maybe ever was
RAM is priced pretty well and compatibility is pretty good with Ryzen 3000. There hasn't been a better time to buy into a platform for a while. AM4 might be on it's way out, though honestly, I don't see most people needing to upgrade from a 3600 anytime soon.
Or, you could even save some cash getting a 2600. Those are also more than enough right now. Just really solid all-around performance, very easy to cool and power-efficient. And good multi-taskers to boot! I ran one myself until recently... mostly got a 3900x to geek-out on. I wanted for nothing with th 2600 but something new to play with. Set up many a system with 2600x's and thus far have only heard praises from the recipients. We're all like you, gaming at 1080p. I also used it for batch photo processing/editing and audio production, which it was just great for. I could stack tracks and instruments pulling tons of samples and doing all of this real-time parallelized audio processing seamlessly, maxing quality on every effect, simulator, and virtual instrument right up to the point when I maxed out my 16gb of ram. Getting an Intel chip that can do that costs a good bit more. We're talking about a CPU that right now, will even handle some decent workstation tasks on the side. Don't let the price fool you! They're gobs more powerful and flexible than your FX. They're inexpensive, but not cheap. It's still a serious midrange CPU that will handle 1080p/60 gaming very well and also offer, I think, a superior desktop experience. Hard to explain... everything is smooth in ways that are unique to Ryzen. It's a unique architecture with unique advantages, that the whole lines share from top to bottom. Point is, if all you truly ever want to do with this rig is play games and have a really nice experience just using the machine, the 2600 is $120 very well-spent.
And later on when they're cheaper, you can easily swap-in a Ryzen 3000 chip for another serious upgrade. I'm running a 3900x in a board that was around when Ryzen was brand new. But really, you may never find a need to. Depends on what kind of gaming you do. There may come a time when some games >60FPS need more than the 2000 series has to give in clocks and IPC. In that event, a quick swap to a 3000-series chip in that same board comes to the rescue. Otherwise I don't see an absolute need. It's nice that you can, though. You're not totally locked-in if you go that way.
Like, for the price, you can go right to the 3600 and never worry, but in my opinion and experience, it's not an absolute need if your goal is to do this on a tight budget. My mindset has always been "Spend the money now, not later." so I'd lean towards the newer CPU, but in this case I can't legitimately say that's the only way to go.
The 280x should carry you until you can save for a new GPU. 2060 isn't a bad choice. I have one. It runs everything at high or ultra 1080/60 with breathing room. Bordering on overkill. I could up refresh rate or go to 1440p and lose nothing. Or with some compromises even run some games at 4k. If you wanna game at 1080p that'll do it for a while! No doubt lol. Nothing but good things to say about it. I enjoy dabbling in the RTX stuff, too. Though honestly if you're not, you might be overpaying buying one for 1080p gaming. When I bought mine it was the best option. Not so much now.
By the time you save enough there's a good chance there will be better options. 5700 is even better, but again... we're kind of in a middle pocket with GPU's right now. Whatever you buy at this point is about to be trumped in value, if not performance as well.
That said, thebluebumblebee also made a great reccomendation for something that's actually great for 1080p gaming, right now. It's still a major, major upgrade for you. Honestly not a bad way to go, either. 1660 super is a killer 1080p card and you're not paying the RTX markup. They can also run cooler and more efficiently, if you care about stuff like that.