With an HD5970, you can get a 30" if you really want to. You can visually tell the difference when comparing 2560x1600 to a 1920x1200, but by no means is 1920x1200 inefficient for gaming. If it wasn't for the mass production of 1920x1080 displays (mainly because it has "1080" in it and because it's cheaper), 1920x1200 would've gradually become the next most popular resolution for gamers.
IMO, your 24" is fine for gaming. The gaming experience will probably be the same after a while, but the preference is different for everyone. Like jefe323 recommended, multiple displays would probably be a more interesting experiment.
If I was to get a second display then, which would pair up well with the one I have?
Eyefinity seems pretty fun, it would be hard to get used to though...
Generally, you should get the same monitor you have now, but there have been some great monitors coming out recently. The only problem is that a lot of them are 1920x1080 and will look awkward paired with your 1920x1200.
The monitor you have now isn't all too bad. If you like how it looks, then you should get another one. The thing about monitors is that preferences are visually-based. It's hard to tell if a monitor is for you based on its specs since monitor specs are very misleading. The best thing you can do is go to a local electronics store and look at the monitors. Find the one you like the most that has a 1920x1200 resolution. Sadly, a lot of the mainstream stores, such as BestBuy, rarely carry any 1920x1200. Spec-wise, I'd recommend a monitor with 5ms or lower response time, 1000+:1 STATIC contrast ratio (you don't need a monitor with crazy contrast ratio numbers), and have great reviews.
Is 1900x1080 superior to 1900x1200? I've never even heard of that resolution, always assumed it was 1900x1200 =p
No. Higher resolution is always better because it has more pixels, meaning more space on your screen. A 1920x1080 has 120 fewer vertical pixels than a 1920x1200. 1920x1080 only recently became widely popular because 1, it's cheaper to produce, and 2, the numbers "1080" sells well because it can better relate to Full HD 1080p (even though 1920x1200 clearly can support full HD anyway).