Thing is, pistols only deal something like 2-3 points less damage than an assault rifle, while having the much better reaction rating.
Shotguns may seem expensive TU-wise, but remember that each shot fires three pellets, meaning it should be compared to the rifle's burst fire rather than its single fire. Yeah, the effective range is shorter, but rookies can't hit anything beyond the effective range of a shotgun anyways (and a considerable amount of combat takes place at close range anyways).
Also remember that a better reaction rating not only means they'll take more reaction shots, it also means that they'll trigger fewer reaction shots from the enemy.
I generally give recruits a shotgun to practice with, since it lets them train reactions while still having a chance to deal some decent damage. If their TUs are okay but their accuracy is shit, I'll give them a sniper rifle and set them up somewhere with a decent sight line, so they can take aimed shots while staying way away from the action. The sniper trains accuracy like crazy, but its accuracy bonuses are complete overkill in the hands of someone decent. If someone has sharpshooter stats, I'll give them an assault rifle... Because they're the only ones with the accuracy to make use of the extended range, and the assault rifle will let them overwatch an area, while the sniper has abysmal reactions.
Additionally, a suitably sharp-eyed shooter can fire bursts at very decent ranges, dealing more damage than a single sniper round for fewer TUs.
Oh yeah, also... Don't use frag grenades, they're awful. Next to no suppression and they have a teeny tiny AoE. A flashbang plus a rookie with a shotgun will deal just as much damage, and the banger will almost always disable the enemy better than a damaging grenade would. And, as a bonus, can't directly kill your own dudes with one...