Here is my take on trail cameras. Most brands have some good units and most brands have some crappy units. It may not matter if you pay $50 or $500. A suggestion for a unit made a couple of years ago doesn't help a whole lot unless you can find a version that was made a couple of years ago and not a newer version made a few months ago. Some models may have a multi year production, but actually change from year to year in terms of internal parts and as such, while the model name or number may stay the same, the camera may not.
I have had $80 trail cameras last 5 years. I have had $350 trail cameras that crapped out at 4 months and had to be returned and had the replacement be replaced, despite the fact that an older version of the camera (same model number is still going 6 years later. I now generally don't spend more than $50-80 on a trail camera. I don't do external batteries, but look for a camera that will take thousands of images on a single run of internal batteries and use rechargeable batteries in it.
Over the years, battery power has been reduced from 6 D cells, to 4 D cells, to 6 C cells to 12 AA and now they have cameras that will give you thousands of images and run for months that run on 4 AA batteries. A lot, nowadays, seem to run on 8.
60 feet seems to be typical range of the cameras to activate. You can check places like Trailcamppro for game camera reviews, trigger times, etc. Most have more photographic resolution that your 2 year old smart phone.
As noted above, if you get 2-3 years out of a camera, you are probably don't well. Don't count on it and don't be disappointed if that is all you get.
I am not going to state a particular model because right now I have have 2 cameras running. One is 6 years old and one is 2 years old. I had a newer camera, but squirrels appeared to have chewed through the strap and the camera dropped to the ground. Where it went after is beyond me, but there were frayed strap threads on the tree and ground. This has happened before, but usually the camera doesn't go anywhere. I STRONGLY suggest you wire your camera to the tree to prevent this sort of thing. I got lazy and didn't have wire and lost while playing the odds.
Interesting note, I always try to save the AA rechargeable batteries. They are more valuable to me than the cameras. I mark sets (color coding) and don't mix and match. I have been running some AA camera batteries for 7 years now.
If you have a $100 budget for a trail camera, check reviews on trailcamppro and look on places like Amazon. You can probably get 2 of last year's model for the price of a similar, slightly better version from this year. When you look at reviews, discard all the glowing reviews. They are pretty useless. Look for mentions of any sort of problems or difficulties, particularly anything mentioned by multiple users. Those will be problems you will likely encounter as well.