Gearing is very important. I believe the 34 front ring along with a 11-28 cassette will get you up most hills quite well. I do believe the weight of the bike also makes a very big dfiference. I tried for years to deny the fact that bike weight changes your climbing to any degree. It does.
My main residence is in the Little Rock, AR area, but I have a weekend house in the Ozarks (Bull Shoals, AR) with similar hills. I have found a light agressive road bike simply climbs better than anything else. Also, by staying with a cassette with a 28 you can stay with the road type rear derailluer, which gives you a more responsive shifting action. I am sure some will disagree with my take on the shifting, but that is what I have found on my bikes.