If you're just trying to assemble clips together, use Premiere Pro. After Effects is not made for real time playback of video streams. After Effects is a compositing, visual effects, animation, and motion graphics tool with a focus on pixel-perfect accuracy. AE is not for video editing. As such, it must cache a preview before it plays anything back smoothly.
So, if you are just throwing a clip into AE and hitting spacebar, it is unsurprising that it isn't playing back smoothly right away.
If, however, you have your whole timeline cached (green line over the whole thing) and it's not playing back in real time, you have an issue and we can try to fix it.
I understand that AE is not for putting footage together, but this problem hasn't always been around. For the company I work for, people here do indeed use AE to put together full movies and I've never had an issue. It's not the best obviously, but I feel as AE gets newer, the lag gets worse.
I made a new project, set the comp to 60 fps, did a simple animation with a shape, let the comp cache, and I'm still getting a VERY jittery preview. Resolution of the preview is 1/2 and so is the playback options.
Are you still facing this problem? If not, let us know how you solved it. If so, please let us know so we can assist you further.