You want either a trail bike or a cross country bike. The term "trail bike" tends to be applied to bikes with around five inches suspension travel that are designed for singletrack riding by those who are not necessarily racing, but who just want to get out and have fun. Cross-country bikes tend to be a little more race oriented. These terms are murky at best, and are not used consistently. Trek seems to use them as I've described.
Recreational and sport mountain bikes are typically price point bikes targeted toward non-enthusiasts, and their geometry will target easy singletrack and gravel roads.
Tire size is a religion. 29" tires predominate in racing, and anyone tall should consider the larger size as well. I'm more of a moderate height and have come to prefer the more proportional feel of 26" and 27.5" tires. Larger tires roll over roots and such more easily, but I don't find that to be a deciding factor. The plus-size tires like 27.5+ and even 29+ are a compromise between trail-riding widths and fat-tire widths. Plus tires used to mean 2.8" and 3.0'", but I believe there is a trend downward toward 2.6". Not sure about that, tbh.
Check what others in the club are riding. Ask them the reasoning behind their choices.