Lag Spikes Last Couple of Weeks

I'm in Pensacola, FL and have been having intermittent lag issues for the last couple of weeks. On a least two occasions, including last night I reset both my cable modem and my router. Sometimes it takes a little more time to sync back up.

I have the Preferred package, but I have a son playing LOTRO while I play Minecraft, a son streaming Netflix and the wife on Facebook. I called into tech support yesterday and they said my cable modem was an older model, but they couldn't detect anything wrong. However they did say I couldn't get the best speeds because I have an older modem cable modem. None of this has been a problem till the last couple of weeks.

I also have a Netgear WNDR4300 Wireless Router that is about a year old.

The problem is I don't want to buy a new cable modem just to find out its the router or an outside cable issue. Last time this happened a few years ago it was actually a bigger issue than just my house. 

Again, it was recommended that I buy a new cable modem at the very least to access the higher speeds on the preferred package. I own my current Cable Modem so if I want to go buy another one at Best Buy, Office Depot, or Amazon which ones are compatible?

If I buy or rent the modem/router from Cox is it good for gaming?

Just need to know the right steps to take without wasting unnecessary money.