Buying guns in Estonia is easy. No background checks, save proving that you are mentally sound. Just spit up the euros and you get your piece. Shooting guns is even easier. There are several companies in Tallinn, Estonia that offer gun shooting packages, ranging from a few pistols to the full monty (M4's, AK's, tactical shotguns, and more)
If you are looking for a unique, outside of your comfort zone travel experience, then firing off a few rounds may be for you. Yes, you saw the old medieval town, you spent time in the main square at one of the many restaurants and cafe's. You may have even gone to the art museum or the zoo. But, none of these experiences are as unique and bad #$% as shooting an assault rifle into a pile of wood.
There are three main gun shooting ranges in Tallinn. We recommend Tonde Lasketiir.
They offer a wide variety of shooting packages, everything from just pistols, to the tomb raider package, to the special ops package. Although they are a bit spendy the experience was worth doing once.
They take all levels of shooters, everything from beginner to advanced, and even offer courses for gun licenses and tactical shooting improvement. Why would you need that? You probably won't, but it's good to know that these guys are legit.