Key factors differ somewhat depending on circumstances and application BUT unless you have somewhat or very unusual needs it's more about quality, warranty, trustability, traceability etc. In most applications where you have ample area then a quality product at lowest all up installed $/kW is probably the target.
PV panel quality is usually good nowadays but there are still low quality units and happenstance disasters. You should be able to get 10 year absolute warranties and a minimum Wattage output, falling slightly per year, out to 20 or 25 years. These are usually actually insurance provided by a reputable underwriter who will usually still be there 20 years from now.
I have seen EVA (laminating material) sold in China labelled "China use only". One can only assume what that means (probably correctly) but can also assume that some will get used in export panels.
Hail damage ratings can vary - claims may or may not be reputable. If it matters then provenance of supplier and manufacturer matter. While panels from unknown or little known brands CAN be top class, it is more likely that a known and reputable manufacturer will do better.
Wattage per area usually only matters if area or mounting mass or windage is constrained. So mono or poly crystalline silicon may not matter as far as Watts per size goes. Non silicon panels are in some cases more efficient than crystalline silicon, but many are not. Flexible materials may be lighter weight and allow fitting in unusual areas or allow walk-on surfaces. If these are at added price or lower output they will be useful in only some cases.
Look at thermal specs for power, voltage and current for a range of similar technology products. It should be reasonably safe to assume that they are no worse than the worst, and the spread is not liable to be vast. If you REALLY care about temperature affects then cooling actually works, but usually, adding an extra 10% area is easier and more cost effective.
Compared to aiming at best thermal performance you can almost certainly gain more from keeping panels clean, angling them to suit the output season that you require them to work best at and paying attention to cable sizes, connections and energy storage and transformation efficiencies. Arranging the mountings so the angle can be manually altered a few times over a year can add useful output. Even a summer and winter angle with bolt and spanner adjustment can be worthwhile. (A nephew of mine installed a 10 kW array permanently angled for winter sun as that was when they needed maximum output and summer output would be more than adequate.
If you have eg a yacht where you want to maximise solar energy collected you may want flexible panels with high efficiency that can be laid on every surface and can be walked on with impunity.
Similar for a solar challenge vehicle but "walkability" probably not an issue.
If for an apartment or small home roof where you want max energy then efficiency counts. Back contact silicon wafers give 10-20% more output per area at a significant increase in cost.