If your PC was running better and getting better framerates at one one point of time then it's obviously a software problem. What you have is more than enough to run games like CS:GO and TF2. It may be low end but I've seen those games run on worse that what you have.
You should be getting a minimum of 70-80fps in CS:GO with that card. Your average framerates would be higher than that. This isn't great considering that it's CS:GO but those numbers are a lot higher than what you say you're getting. I can pair an R7 250 with an old dual core Athlon II or 64 CPU at 3ghz and that would be more than enough to run TF2.
I agree that anything less than an RX 570 or 3gb GTX 1060 really wouldn't be worth it. These cards will more than double what the R7 260x is capable of getting. Normally I would recommend the RX 570 to you but those cards are still not at their April/early May price levels, which are $180 to $190. The 3gb GTX 1060 is a little more reasonable. You could also look at a used GTX 970 if you can get one for under $150 or less, but a GTX 970 needs a power supply with two 6-pin PCI-E power connectors.
You need a 450w or better power supply with a 6-pin PCI-E power connector for these cards. If you do not have a large enough power supply, then you can look at the 520w Seasonic m12II or the grey label Corsair CX550 550w. Generally the 450w power supplies on the market aren't a very good value and most of them aren't well made. Also, a 550w power supply is enough to handle higher end cards, which gives you more room for future upgrades.
Later down the line you can look at upgrading the CPU, RAM, Motherboard, and OS, but I suggest waiting until March or April to do this. AMD will have their 12nm version of Ryzen out, called Pinnacle Ridge, which should have higher clock speeds and hopefully other improvements. Also, Intel will have it's full line of 8th Generation processors and 300 series motherboards out by then.
People love playing CS:GO, TF2 and other First Person shooter games with a 144hz monitor. If you have the money, you can ultimately upgrade your PC to run at a high framerate. A CPU like the Core i5-8600k or maybe even the Core i3-8350k would be good for that. If you're fine with a 60hz monitor then you don't need to swing for the fences. What you upgrade to should depend on what framerates and settings you want in your games.