It is best to look at benchmarks and see what the actual performance numbers are like for indvidual cards, rather than using the naming schemes AMD/nvidia use. They are pretty confusing and meaningless, except when you're comparing GPUs within a single make and generation of graphics cards. I would recommend review benchmarks from Techpowerup as they benchmark a wide range of cards at various resolutions and then give useful summaries. For example, try this review:
http://www.techpowerup.com/reviews/NVIDIA/GeForce_GTX_Titan/27.html
Also Anandtech have useful GPU benchmark comparision site:
http://www.anandtech.com/bench/GPU12/372
In terms of compatibility with games, it's mostly a question of what DirectX level the game can run at and what DirectX level the graphics card supports. Most games these days have backwards compatibility with DX9 and DX10, so you should be ok with pretty much any card thats come out in the last 5-7 years. That said, it would make no sense to get a graphics card that is anything less than DX11 capable, as the cards that support anything less are really slow and outdated anyway.
The video RAM requirements are pretty straightforward. For current games, you want at the very least 1GB, with 2GB/3GB being the sweet spot. This would be for 1080p resolution and medium, high settings in a paticular game. For higher resolutions and more premium quality settings (e.g. high levels of anti-aliasing), you will definitely want at least 2GB.
You will also of course need to take into account the rest of your system. A good system will have well matched CPU, RAM and GPU. There's no point having a very fast GPU if your CPU is too slow to feed it enough data, etc. For this it would be best to ask here for a system spec for a given budget.
For starters, you're current HD2400 is way too slow for pretty much any recent game, even the less intensive games. Those that do run, will look like very poor and at low fps. Therefore, it's not just a case of will the graphics card run the game, but how well it can run it. Even a budget laptop will run the latest game, but it certainly won't be anything near playable.