It is all down to personal preference but a method I found very effective, is to start with the acapella (assuming you are wanting to remix a vocal track). Select which part of the vocals you want to have as a vocal shout before the drop and work that into a build. Starting with a build is a very unusual technique as commonly people start with the drop, however when making a remix, the drop has to sound good and link in with the vocals. Keep experimenting until you have a drop that works with the vocals and then build the rest of the track around that. Generally when I make remixes, I only use the vocals and nothing else, that still keeps essentials from the original while allowing me to turn it into my own song. I find remixes that are exactly the same as the original but with a different drop, intro & outro, very repetitive and really not very impressive, but if you're inexperienced in remixes it can be good to start out.
Hope some of this helps,
Harwood