Just buy a decent router. I took the plunge and never looked back.
My Nighthawk gaming router, allows merging of both signals, so no seperate SSID's and it auto detects and connects to correct wifi.
Wii and PSP was worst for router connection, I used to have to mess around to get them to connect. Now they just instantly connects with no issues (even though its pointless now). Yes, I still use my PSP's.
Sorry OP, dragging this off topic.
That’s all well and good with WPA. But a lot of newer routers these days will give you a hard time with connecting. Plenty of documented incidents of these. This is due to higher security standards being put in place.