We are doing cloth also, but we've been using a SimpleHuman trash can to store the dirty diapers between washes and have been happy with it. We chuck some baking soda in every few diaper changes to keep the odor under control. The SH has a nice close fitting lid. We already had it for our kitchen, then found a knockoff version on the street, so the knockoff became our kitchen trash and the SH became diaper trash. Some neighbors gave us a diaper genie and to be honest I found it to be a HUGE pain as the opening was not really large enough to accommodate the diaper easily, so I was always getting wet diaper up past my wrist (and yes, I washed my hands afterwards, but it still grossed me out, and was just more of a pain). That might be less of an issue with disposables as they are smaller. Our daycare also uses a regular trash can (with a heavy and close fitting lid) for their disposable diapers...they've been in business 20+ years and have presumably dealt with a lot of diapers so if they have not found a fancy diaper pail with special deodorizing products to be a necessity...
When the babies are just drinking breastmilk/formula, their poop really does not smell much, so as long as you are taking the diapers out to your trash pickup bin regularly you should be fine. The poop does seem to smell more post-solids but it's still not (IMHO) a very strong smell (though with cloth, we are flushing the vast majority of the poop down the toilet so it isn't sitting in the bin. I guess you could try that with disposables also if you didn't want to empty the diaper trash as often?). So I would say you are fine to at least initially try a regular trash can. You can always buy a diaper-specific product later if the trash can option is not working out!