I would suggest doing full body (or in your case full upper body) workouts in the form of either compound lifts (deadlifts, bench) or a form of bodyweight exercises (i.e. calisthenics). Here's why;
Both compound lifts and calisthenics incorporate multiple muscle groups during exercises rather than just one. They also both stimulate the use of the core in a lot of exercises. Having a strong core is very beneficial when riding a bike, so this will carry over to a better cycling performance and/or experience.
Both compound lifts and calisthenics will also give you functional strength rather when compared to bodybuilding style lifting.
The only downside with all of this is that you're going to gain some weight, assuming you're fat % stays the same and your muscle mass is going to increase. This isn't a bad thing during flat rides but if you want to do some cycling in a more hilly terrain, you'll notice that you're heavier than before.
I personally do all of the above, compound lifts, calisthenics and cycling and I can say, on flat rides having the extra weight has been a bonus for me. I have more power and balance on my bike. In the mountains I can definitely feel that I've become heavier which is alright because I don't race in the mountains anyway, I only go there to train and have fun.
Most (if not all) pro cyclists also combine compound lifts and bodyweight exercises to train their legs and core for extra power in the legs and extra balance on the bike (a lot of balance comes from your core).