I'd have to say that the Ebonite Tornado, Brunswick Avalanche series, Brunswick Power Groove, Hammer Vibe series, AMF (Global 900) Reactive Angles and Storm "Tropical Storms" would suffice for a beginning bowler searching for a 1st time bowling ball. Since you are talking about throwing both a left and right handed delivery, I believe you're ambedextrous. It definitely is possible to bowl with one bowling ball with two different hands, because I am also ambedextrous, but I only use my left handed delivery during non-sanctioned leagues and during practice.
Most of my bowling balls are drilled with the exotic "RICO" (named for Rick Hamlin, a Brunswick staffer) drilling that has the "pin" in the palm for more control, but also enhancing the overall performance of the bowling as it travels down the lane. Anyways, the tech aspect of a ball's drilling may be too advanced for a beginner, but when you learn more about the game, it may be beneficial to know.
Just ask your local pro shop staff about what type of bowling ball would match your delivery style, the lane conditions you mostly bowl on and the budget you have for purchasing a new bowling ball. When you've decided on the ball, they will measure your hand and span, then will apply the measurements to the bowling ball when drilling the holes out. They may also ask you if you would like plastic or rubber finger grips that are soft and may help you hold onto the ball much better during approach and delivery. After they're done, if they're located in a bowling center, they will bring you out to a lane and have you try the ball out for a few frames, then they'll ask you if it's comfortable and if not, they'll adjust it for you.
Good luck and enjoy!