The 3100 is the weaker of the two newer R3s due to it's split CCX setup.
The 2600 would be my choice here - You'd expect similar gaming performance from either chip, when <8threads are required, with a slight edge to the 2600. In titles that utilize >8threads (either now or in future), the 2600 will outperform.
As a 'budget' option, the R3 3300X would've been worth considering (4c/8t) as it's matching or bettering an i7-7700K, but I don't remember the last time a 3300X was available anywhere close to it's $120 MSRP.