Try playing along to something like Crazy by Gnarles Barkley; it's in common time, the tempo is in the moderato range (i.e. not too slow, not too fast) and it's quite short. Plus the drum part doesn't really change so you can just practice a solid 1/8th note groove for 3 minutes and concentrate on making that sound tight and musical.
I'm sure there are other similar tunes - one that springs to mind would be Billy Jean by Michael Jackson. That's a little slower but has a very strong groove and even if you just play a completely straight groove for the whole song it will sound fine.
I think this is the best thing to do for a total beginner. Pick tunes that are moderately paced in common time and just practice a basic 1/8th note groove. Doesn't matter if you can't do any fills, just keep good time and the rest will come. It's also useful if the song has occasional breaks where the drums don't play so you can practice stopping and coming back in on the beat etc. Something like Black Magic Woman by Fleetwood Mac does that a lot as I recall, but I'm sure others would have better suggestions.
Good luck and have fun.