Although a lot of reggae drummers play without the strainer, there are also quite a lot of them who play with it, it just shouldnt be tightened too hard. My preferred snare is the Trick 10 Lug because of its high tuning wich is far more important for a characteristic reggae sound, i also use the picollo or sometimes a combination of the Bleifuss (for Rimclicks only) and the DW (for everything else). Also the bamboo snare from the signature snares extension pack is very useful for fills, but i wouldnt use that as my main snare. But oposed to what jhonvargas said, if your going after any reggae-type of sound, then by any means, dont dampen the snare, at least not for the fills! (Btw i dont think latin and reggae are similar at all) However the suggestion of using only or mainly the top mic is often a good idea. Another important thing are the articulations: basically there are only 2 of them wich are used in reggae, the rimclick/sidestick for the main rhythm, and the half-edge for the fills. actually reggae drummers play the fills very colse to the rim, but even with the half-edge you can get a good sound - after all we have to use what we have at our disposal. Also the drag and the flam can be very useful as they will sound more natural than individual hits played very fast. Depending on wich snare you use the rimshot can have a nice high-pitch, timbale-like sound too - try this on the Trick snare with low velocity!
As for processing, use some compression to give it more sustain, but dont set the attack time too short so the transient will remain uneffected and dont compress to hard - retaining the natural dynamics is a key point for mixing reggae drums. On the EQ side i usually boost a little bit around 500Hz, and i often cut some lows to clean things up, specially if the kick has a pronaunced click. For the top end, its really depending on the context, boosting can help for more definition, but it will also bring out the sound of the strainer, so if you think you have too much snare ringing, you can try cutting a bit, but be careful not to make the sound too dull.
And finally, add some tape delay and a dirty sounding spring reverb.
As for the rest of the drums, i usually use the pearl masterworks for kick and rack-toms (if i ever use a floortom i prefer the Ludwig Vistalite) and the sabian AA hats. The pork pie kick is nice too, specially if the bass isnt too deep.
But after all, reggae is about the player, not about gear, so a key element is your composition, specially on the fills - if theres a crash, it will often be at the beginning of the fill, rather than at the end on the first beat of the next measure for example. Try also the open hat for this. Also the fills should be played at much higher velocities than the rest - the difference is way bigger than in rock music.
I hope this helps