I will respectfully run against the grain and recommend the 48, given your purpose. This is going to be based on my experience with the brands you mention. I have a 48 in .20 like Jeff, a 34 and a Lightning in .22, and I have gotten to shoot a 54 although I don't own one.
For bench shooting my 48 willshoot at least aswell asthe BSA and has a better trigger. It is one of the few rifles I am choosing to shoot with iron sights for now, because I like thesights it came withThe Lightning can be tuned, but mine is not. The BSA trigger is complex and not a DIY project for my meager skills. The 48 is a big heavy rifle, and the BSA is a short light carbine. For hunting I would want the BSA but for target I like the 48.
I did not care for the recoilless operation of the 54. I think it is too mechanical for my taste, meaning more stuff is moving around. It is a scope killer because it is recoilless to the shooter, but not to the scope, which rides back on the carriage when you shoot and takes the shock of the sudden stop. It is even heavier than the 48. Both are really well-made rifles... the 48 is just more tomy personal taste. With the 48 you would get a quality scope and a very good scope mount, and you'll be fine. The 48 is just a magnum springer when all is said and done, and not even at the high end of what is considered "magnum" any more. With the 54 it seems that additional measures are necessary to keep the mount from moving and you'd want an even better built scope, due to the recoiling carriage.
I think the 52 is the jazzed up 48 in appearance, which is fine if you like elaboratecheckering and stuff. The 54 is the recoilless version of them.
I also really love my 34 and as a field gun I could pick up either the BSA or it, and be just as happy. It is longer than the BSA but a comfortable weight for walking all day. It is also accurate and has a nice trigger, but I don't think it is quite in the same accuracy league as the 48.
Frankly I kind of like side lever guns. I don't necessarily prefer them to break barrels, but if you already have some break barrels and want to try something a little different, the side lever is nice for bench and bipod use. I don't personally like underlevers as well.
I will qualify this by saying they are just my personal experience based on the guns I happen to have. I think I need to spend some $$$ to get my Lightning tuned by a pro, and I just haven't gotten around to that. It certainly has potential, but they are not cheap to have work done on. The 48 is the "Yard Commander" meaning it is a cool bench gun and will also strike unwelcome visitors with ease and authority.
And to make matters worse, I would add to your dilemma by suggesting you also consider a Cometa (either Fenix 400 or the new Fusion)... I only have the old RWS94 versions but I just freakin' love this break barrel and the new ones are even better. You could buy some pretty nice glass with the savings.