Note that the OP is asking for a DAW to create and edit DJ mixes, not make tracks. I asked a similar question a while back (I also want to make DJ edits of tracks), and while the default answer seems to be to get Ableton Live, someone was kind enough to post a list of alternatives.
I went through and tried all of them (that had trial versions for Windows – on a Mac or Linux there are other choices), and the only one that approached beat gridding in a DJ-friendly manner was Presonus Studio One. However, the beat grid feature is only available in the Pro versions which aren’t cheap, and also effects only seem to apply to entire tracks, which is also not a DJ style workflow.
On my old computer a decade ago I had a copy of MixMeister which I played around with, but since then development seems to have stopped. So, I’ve decided that although it’s expensive, it’s best to save up and invest in Ableton, which will do way more than I need now but allow plenty of room to grow in the future.