I would agree with the other comments in this thread on separating the router from the wireless access point. Separate devices, while costing more to obtain, provide more flexibility in placement and unique upgrade paths for each device.
I have seen a few "retail" routers (1 WAN, 4 GigE on common LAN switch & common IP network; basically a 2-port firewall connected to a 5-port Layer 2 GigE switch) from Ubiquiti in the range of 100 USD to 150 USD. A friend of mine bought the Ubiquiti USG model (it matched his needs) and had issues with the console port & management interface when he first set it up, but he eventually resolved those issues and still likes the product.
If you have some spare PC hardware (what I did initially), or can obtain some unused hardware, then you could build your own using "smoothwall", "ipcop", or "pfSense" software packages; they are based on either Linux or FreeBSD OS. If you do build your own router/firewall, look at power consumption, heat generation, and noise requirements since the machine will be one all of the time. All 3 software packages have useful "web GUI" for managing the router/firewall and reporting on stuff. Also be thoughtful regarding what else you plan to do with that router as "more flexible and more services integrated into the router/firewall equals larger 'attack surface' and related security holes".
I like the idea of separating the wireless access point from the router because it gives you the opportunity to place the access point in an optimal location to serve the entire house. The thought being that the router might not be in an optimal location for a wireless access point; I know that my router is not optimally located within my house to support a co-located wireless access point. If coverage is still "so so" after installing a separate wireless access point in your house, then time & budget can help dictate when a second point can be added elsewhere within the house to improve coverage.
Any range & throughput issues are going to be impacted by house construction and signal interference; houses are not "RF transparent" as transmission frequencies increase (why LTE services are in the 600 & 700 MHz bands). You did say that you find external (meaning "not yours") wireless signals within your house. In cases where "RF congestion" exists, picking different channels and experimenting is key. It helps to understand how the channel positions (actually "center" or "peak" of the channel frequency) 802.11 wireless bands work, but you should still expect some "throughput degradation". Some "homework" (aka "research") might be necessary.
I like the fact that you are using the Powerline networking option. Some Powerline products can be "networked" so you can use 3 or more of the same technology & security key to create a "shared LAN" environment over the power lines. I found the Powerline solution useful in my own house, even using 2 different Powerline technologies & different security keys at the same time without issues. I did that until I found time to drag cables where I wanted them. I prefer wired over wireless; that's so "old school", right?
I also recognize that budget and/or "WAF" ("wife acceptance factor") also have to be considered.
I used to do networking & network security for a living. Now I just do it for fun, but I still take it seriously.