My (and many trainers) preferred foundation bit is some form of cheeked snaffle. These bits add pressure to the offside of the nose, and prevent the bit from pulling through the horse’s mouth. The “usual suspects” are fullcheeks, dee rings, eggbutts, and for western the offset dee.
All of these bits function in essentially the same way if they have the same mouthpiece. I prefer french links, as they prevent the mouthpiece from raising into the palette and they give a clearer differentiation between each rein. The “comfort snaffle” and similar mouthpieces correct some of the problems with a single jointed bit, but do not afford the nuance of the french link due to their stiffer nature. In some cases this can be a benefit, but they are not as clear a signal to the horse. Of these cheeks, I prefer the eggbutt as they tend not to flip forward like the dee and don’t need keepers like the full cheek. All these preferences aside, I tend to use a lot of plain single-jointed dees and full cheeks because they are far cheaper and work well for most horses and riders.