If you have to compete with lots of other users on the band then maybe you should look for a higher power router.
Something that outputs 200mW instead of the usual 60mW
We are not allowed such high transmit power levels.
Which is good, because it is one of the most foolish things you can do to try to "solve" interference with other nearby WiFi access points. Doing so pretty much ensures that your neighbors will try to escalate. Some of them may do it with a hack to override firmware limits, which is likely to lead to a louder more distorted signal. Whatever they do, any advantage one gains will be short lived.
If negotiating with neighbors around a better channel allocation is impossible or undesirable, then getting a working 5GHz solution is a much better route. Their are fewer 5GHz devices, more bandwidth/channels available (in the US, at least), and because the range is somewhat lower, less chance of interference from nearby APs.
Beyond that, putting your AP on the same channel as other APs in the area can actually be more reliable, because in that situation, the competing APs should actually listen for one another and avoid transmitting over eachother, whereas picking a different (but overlapping channel) will just lead to bandwidth killing interference.
As for what router. I've been using a now obsolete Netgear WNDR3800 (same basic hardware as the WNDR3700) running OpernWRT for years and it has worked well. One of the nice things about OpenWRT is that it implements proper QoS techniques for the broadband connection. You do have to configure it with the right upstream rate, but once you've done so, it provides consistent, low, ping times even when a big upload is running.
I have a TPLink Archer C7 running OpenWRT yet that I haven't deployed yet. What model TP-Link router do you have? You might try running OpenWRT on it if it is compatible.
If I were going to buy something that I wanted confidence would work without a lot of tinkering, I'd probably get an Apple AirPort Extreme or Express. We are a mostly Apple house though, but compatibility with other devices should be quite good. You can probably find a refurb in your price range.