Other well-reviewed tires:
BFGoodrich Advantage T/A
Bridgestone Dueler H/L Alenza
Bridgestone Turanza Serenity
Continental ContiProContact SSR
Continental ExtremeContact DW(S)
General Altimax HP
General Exclaim UHP
Goodyear Assurance TripleTred
Kumho Road Venture APT KL51
Kumho Ecsta LX Platinum
Michelin Primacy MXV4
Do you have a favorite brand? Check them out first. If not, and you're looking for an economical option, consider Kumho. Seeing as they're designed/manufactured in Korea, they're kind of a natural fit for the Genesis, I think.
If you're at all looking for "performance" rubbers, I would recommend looking at Continental's ExtremeContact line (either DW or DWS) -- assuming they'll fit your model of Genesis'
rims. These tires are getting rave reviews from Tirerack users and also from folks on this very forum.
Otherwise, compare tires based on what you consider important. All these tires get "very good" or better reviews overall, so you're not likely to find a dud in the bunch. Of course they have very different strengths and weaknesses. Be sure to factor in wet and snowy/icy traction results by considering how likely you are to be driving in these conditions on a semi-regular basis in the next 6 months.