You don't say how much weight you're lifting. There are two basic types of barbells -- the thicker ones you see at the gym at the bench press and the thinner ones for free weights. But a lot of people use the thicker ones for the types of lifting you were doing because it's kind of a power lifter kind of thing and if you get far up there in weight you need a very sturdy bar. They are different, and the grip can really be quite different which has nothing to do with quality of the bar but with the style the designer of the bar is looking for. The problem is looking around for these these days -- most people are now buying on the internet, which has caused stores to carry one or at most two brands of anything while there are a lot of brands out there. I tend to buy on the internet from the outfit that supplies Gold's Gym because I use Gold's and have tested things out there. Their supplier is called Power Systems, I think, and anyone can buy from them. But you won't be able to test it out first unless you go to a store and then you're back at today's reality, which is that stores don't carry much variety anymore because of competition from the internet. But again, it all depends on how much weight you intend to end up lifting, because if it's only going to be relatively light weights -- not power lifting -- those bars aren't as wide to begin with. I'm not sure personally that's really an issue in the long run, the bigger issue is the comfort of the bar -- the roughness even if you're wearing gloves. I'm not a serious weight lifter -- in fact I can't really go to the gym now because of pain issues from exercising a lot and then I got old and broken -- so perhaps the best thing to do is at the gym find someone who's a really juicer with muscles bulging out the sides of his or her head and ask them if they have a recommendation.
Hey, good for you! It's cool when you find a new activity like that that you really like. I have some of these bars at home. Mine are weighted bars. Are you talking weighted bars or are these the type you put weights on? There are definitely different types of bar bells and finding what is comfortable in your grip is important. Girth probably doesn't matter for the work out but is more about your comfort. I find that it is like anything else weight lifting related. As I do it, I get stronger and can increase the weight involved. BUT, the way it feels in your hands is probably not going to change so--- find a set that feels comfortable to you. I like resell places (like Play it Again Sports which is a chain) or you could try Dicks to get a feel and then look online for something similar. (cheaper.)
If your hand wasn't comfortable, I do think it would impact your work out. :>) good luck and keep up the good work