I recently had issues with the wifi adapter that comes with my laptop model (Ralink RT3290LE) and I discovered that it's an issue if your modem/router is a Cisco which is what my ISP is providing. At the end I bought my own router and was able to connect to the internet.
I want o avoid these kind of problems in the future though and I would like to know what kind of replacement I can get for my lapto that are compatible and also if there is a compatible wifi adapter that also has AC network along with b/g/n.
It says not compatible with HP, but that applies to slightly older models that still had a BIOS wifi whitelist which yours does not. We have done some experiments here at the Forum and have shown that the whitelist has been gone since before your laptop was manufactured.
Having said you can do the upgrade you might want to see how to do it. See page 52 of the Manual here: