Just checking back in to let everybody know what I decided to do in the end, should anyone be interested.
I've bought a TP-Link Gigabit router, and simply configured as an access point. I specifically chose this router because it's cheap and easily flashable with dd-wrt or openwrt should this be necessary. The stock firmware did it needed to do for my needs though, so I just used that.

Total cost: 45 euro, and works perfectly! 5/5 Wlan coverage throughout the entire house now. I'm happy!