Trail cameras all have a fairly limited range - many people seem to expect much more than they can deliver. In general the ideal "viewing" distance for them tends to be about 10 - 20 feet. Given this you can't easily cover huge areas with them very well and so you have to have a plan to photograph your target fairly close to the camera.
For me trigger speed is a big factor, as is the quality of the sensing. These two things sort of run in parallel but all cameras miss triggers it is just that some miss them more than others and, of course, if you never see it then you never know that you missed it so you need to have confidence in the sensing. When it comes to trigger speed then I think this is important due to the fact that most cameras take their best photos pretty close up and so you need a fast trigger time to catch a moving deer in that sweet spot. Many cameras turn in a lot of empty photos because they take several seconds to trigger and the animal has already left the frame before the photo or video gets taken. If you are baiting deer into a feeder for example, where they might stand around for a while, then trigger speed becomes less important but be warned - I tried to bait sika in with wheat and various other stuff and they were frightened by the wheat on the ground and moved away never to be seen again
It is sometimes possible to buy "old stock" cameras at much reduced prices - for example I tend to buy older Bushnell cameras as the price is reasonable and they have everything I need. The 2012 Bushnells have the 0.6 second trigger so I wouldn't buy anything earlier than that. I think only Reconyx can match that, even in 2014, but they are far too expensive to tie to a tree. (the 2014 Bushnells are down to 0.2 seconds trigger time but are still too expensive for me) However, buying a secondhand trail camera doesn't seem like a good idea as they all have a limited life - any complex electronics you leave out in the weather 365 days per year in a cheap plastic box is on borrowed time and 2 years seems about average for a trail camera.
In as far as I can see all cameras have various bugs and faults so it would be worth making sure that any camera is suitable for your requirements - for example on some models of Bushnell the "field scan" (Bushnell speak for a timelapse system) never really worked very well so you don't want one of those if you need timelapse. The internet is a good source of common faults and bugs for the more popular cameras.
Swing by the chasing game forum as those folks know all there is to know about trail cameras:
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