I've had lower back issues for years. In the past I was good about going to the gym and working on my core strength and this did an excellent job of keeping the lower back pain away. However, over the last few years I have been lax in going to the gym (read: I cancelled my membership and don't plan to re-up). Due to my lack of working on core strength my lower back pain has been creeping back and now I need to address it again.

I'm thinking about buying a stability ball and using that at home to do core work 2 or three days a week for half an hour or so. Does anyone have any success stories using one of these balls for core work? Does anyone have any suggestions for exercises to do? I found this link with three simple exercises that I may try. Would these three alone be enough to improve and maintain core strength?

Also, what is the key to deciding what size stability ball to buy?

I'd personally spend 20 bucks on some resistance bands and do:

banded good mornings
pull throughs w/ bands
leg raises
planks
pushups

Only one of those appears to actually focus on the core...

the good mornings work the lower back which is part of the core
the pull throughs work the lower back (core) and the glutes/hamstrings which cyclists typically neglect
leg raises work the abdominals/obliques
planks work just about the whole core
and pushups require an engaged core to do properly, with the added benefit of improving upper body strength a bit.

If you think flopping around on a stability ball is the way to go, by all means. I was just trying to offer suggestions, I've been lifting pretty seriously for about 4 years and was trying to address the issue you're having. The three things you posted will definitely help improve your core as well. Just offering an alternative (or better yet an additive that addresses some other areas).

Are you sure it's not a mobility/bike fit issue?

I might consider adding them as a whole along with some flopping around.

I do sit at a desk for a living so I am not as mobile as I should be, but my bike fit is fine.

I do these exercises and they've helped me. The first time I did the #1 exercise with the crunch circles on the ball, I could barely make it to 10 reps and felt like I was going to throw up. I've improved quite a bit since then.

I know the feeling. Being a desk jockey has definitely given me some tight hamstrings and lower back pain before.

Do you use a foam roller? They're really helpful.
Not sure how cool your boss is, but I've heard people say that sitting on a large mobility ball instead of a chair requires you to keep your core engaged during the way and can help alleviate some issues. I've always wanted to try it.

These look like good options.

One of my old bosses did that at a prior job.

using a stability ball as chair at work helps me..... may not work depending on what you are doing for a living sitting at a desk

I do hanging leg raises, ab wheel rollouts and kettlebell swings for my core.