Drums normally need to be treated as part of a collective whole when it comes to making them blend "into," the music.
This usually involves careful use of an EQ, my favorite currently is Fab Filter Pro Q.
As well a compressor definitely helps to bring out transients in different ways that make the drums sit better in a mix as well.
There is an entire world of theory, application and discussion about compression, but I won't bother trying to go into depth.
If your song has a bass line then the kick and the bass need to co exist peacefully. EQ IMHO is much more important than compression in this situation. Compression is just going to showcase how good of a job you did or didn't do with your EQ.
If you use 808s you MUST be careful with the ones with long tails, the subsonic freqs can eat up a shit ton of headroom, you need to carefully EQ these kicks not just for a "blended," sound but also overall headroom in the mix, so that you can present the frequencies of the 808 that matter but also so that the garbage in the sample doesn't put your mix in park headroom wise. A properly EQ'd 808 will hit and have body however, leave room for everything else. This is part of the issue that you speak of regarding muddying up the mix.
Learning how to do this is not something you learn over night and if you are in a hurry to get these instrumentals/songs put together you are much better off hiring a mixing engineer who can get the job done quickly and make you sound like God among men
Peace
Illumination