Shiley and Bivona are the two most common brands on the market, with no real practical difference.
When transporting a trach patient one of the most important things to remember is to have a trach of the same size and half a size smaller, just in case you end up in a situation where there is total plugging you are unable to relieve with suction.
Generally, in my experience, when a trach comes out, your best bet is to go with the half size smaller immediately. The stoma that the trach is in closes fairly rapidly, and the tissue surrounding the stoma is very tough and scarred (not very stretchy) so working a new trach in if you are not experienced is going to be difficult.
What the poster said above about sterile water or sterile NS is very true. These patient have extremely thick secretions and a good lavage is sometimes necessary.
If all else fails and you are unable to ventilate through the trach (total occlusion) your best bet is probably to completely remove it, occlude the stoma, and bag the patient through the mouth and nose with a BVM as usual. I know this doesn't sound ideal, but it beats the situation you may currently find yourself in.
The patients we see who have trachs typically get them because of chronic pulmonary infections, inability to control secretions, poor tracheal stability, etc. These are mostly seen in peds. With adults, you could see your cancer patient, trauma patient, or other type of patient whose hypopharynx or upper airway may have been destroyed for some reason.
As is the norm with most chronic patients, either them, or their caretaker is probably very knowledgable about hwo to manage their current condition. I remember when I first started as a paramedic allowing a mother to ride int he back with a trach patient because she was really the ideal person to manage it at that time. The patient was more comfortable with her suctioning, she had better technique, and it made me more comfortable. Nowadays, since I have some more experience, I am still no opposed to doing that.
I will also add, I agree completely with MSDelta, proper suctioning is very important, and unfortunately not done very often. In fact I went to a referral the other day for a child with RSV (not a trach patient, so sorry to get off topic) and the child was full of secretions. We asked the referral nurse if they suctioned, and she flat out said "We don't do deep suctioning here." Kind of scary really...a child in respiratory distress, and they simply don't treat it because they are not comfortable with proper suctioning. Oh well...