10 years ago we initiated a TSI plan with the primary goal of improving the timber quality, species mix, and longterm value (both financial and wildlife). Crop trees are oak (white, red, cherrybark, nuttall), poplar, black cherry, loblolly and shortleaf pine, and the occasional sweetgum. We sought out these species with good form, considered their position in the stand, spacing, and released based on touching crowns.
We took a hybrid approach with the competing junk/undesirable trees: felled, girdled, basal spray, and hack'n squirt. Chemical applications work really well for smooth/thin bark trees. It takes a few years but the remaining crop trees really responded well and jumped up in height and out in crown.
1) Form and/or position in the stand. If you have lots of multi-stemmed trees or areas of overstocking, sometimes you must decide which trees to remove simply to decrease competition. Low forks, excessive sweep, injury, and branching can all help determine which to keep vs. remove.
2) Shade tolerance. When you open up the timber and sunlight hits the ground some of those stumps will sprout and some will not. Do a quick search on "shade tolerant tree species" to help guide in this regard.
3) Although gums aren't the most highly valued, they'll still make a log one day and depending on your regional market they're worth something even if it's just pulp. I won't cut a gum "just because it's a gum" if there's no other crop trees around.
4) Safety. Flying along felling "little stuff" it's easy for the focus on safety to fade a little as the day wears on. Vines connecting trees can easily pull the 3-5" diameter tree you cut a moment ago with the tree you are currently felling. Little stumps left even an inch or two above the ground but still hidden by leaves can be tripping hazards. Felled saplings especially in severely overstocked stands are prone to hanging/lodging. Just because it's small diameter doesn't mean it's not hazard.