HD TV viability for PC gaming.

Hi I'm planning on upgrading from my Xpotato to a gaming pc. Obviously I'm on a budget but want to put as much as I can into the tower as possible. I'm wondering I need to invest in a separate monitor now or if one of my TVs will be sufficient. I have two one is a 52" and the other is a 32" both are 1080p 60 hertz. I was thinking about using the 32". Would this be viable? It seems to work fine with my xbox one but I don't want to miss out on superior graphics due to my tv. I'm thinking about spending about $1200 u.s. on system preferably most of that just on the tower.