I've used black, white and red primer before (black from GW, others from Halford's) and I've found that GW paint adheres well to them all.
The red is particularly useful as, whilst not the red I want to end up with, it's a good basecoat so I can quickly overbrush some blood red (or whatever the modern equivalent is called) and then paint in the areas that need it (such as the joins in the knees).
I've also used some gloss paints that have been custom mixed and they are very shiny... too shiny for warhammer models IMO. However, if you don't mind shiny (and you intend to put a thin layer of varnish on the model once done so that it's all similarly shiny) then they work alright. However, they need to be sprayed on top of primer (so you still need a black/red/white/grey primer) but you can get very accurate colour replication. I've not had much issue with paint losing adhesion but I've never put these models through the wear and tear of rubbing up against foam in a case...
The only spray I currently suggest avoiding is the Halford's Matte Black (not a primer) as the adhesion qualities are poor these days. Varnish would probably help but I never feel my models are finished enough for varnish.
If you can get an airbrush to work then that will give you a much better result in all likelyhood. However it does require a lot of effort in my experience to get the consistency right (eases with practice) and to clean it out. You will still have to prime your model first.