I've always believed that the "lowly" .22 rimfire is the best tool for a novice to become a rifleman. It's also an excellent tool for an experienced rifleman to stay "tuned up".
One part of tight groups is consistency in the sight picture at the time the firing pin hits. Generally, using some sort of steady table as a rest, with sandbags, lets you focus on coordinating the sight picture and the squeezing of the trigger.
It's a learning curve. So, start out easy and then transition to more demanding types of shooting.
You're from BATFE? Come right in! I use all your fine products!