Witch would you buy

I'd buy an underlever because I already have a nice break barrel. I have never owned an underlever so I'd like to try one at least for a while.
One thing about break barrel guns is they are lighter than underlevers or sidelevers and faster to reload for a follow-up shot when needed, so if you plan on hunting this is something to consider, especially if you walk a lot while hunting.
As far as caliber, .177 or .22 will get the job done. 
 
Either type will outshoot the shooter if it's a quality rifle. I think the most important part is whether the rifle fits you, whether it's tuned to its best potential, and whether it is at the appropriate power for your application. Personally, I own a sidelever D48, an underlever HW97 and a break barrel Gamo, because I like them all! :) I grab the rifle that is right for the need of the moment.
 
Do side lever and under lever guns have barrel droop issues?

I had a Trail NP break in .22. that gun ate scopes and sheared the mounting bolts multiple times. Heavier pellets will help combat too high of speed making pellets unstable.

All told, get the one you like and shoot it. The Umarex Swarm looks to be a decent hybrid, multi shot break barrel. For around 200.00 it is worth a look.
 
Gamo Swarm Maxxim is what you mean. Break barrel action utilizing a 10 shot clip. OK accuracy and robust performance is the word on them.

Break barrel and underlever seem to be the most common hunting guns with break barrel taking the lead there. Underlever and side lever both feature fixed barrels, leading many bench shooters to consider them superior target guns. For springer guns .25 caliber is generally considered the largest hunting or pesting caliber of use, though you can now find a few models that run to .30 caliber. For small pests and most birds a .177 is a proven performer; the .22 is of course the long-time go-to caliber for most air gun shooters whether pesting, hunting, or target shooting.

The general rule is to buy the best quality you can manage, even if saving up for a while is required. That said, I am a HUGE fan of the lower priced guns for people just getting into air gunning because you can get reliable, accurate guns for under $150 by shopping around. Be aware that there are guns that while costing about $100 more will deliver superior accuracy and in some cases durability. You get to decide for yourself what suits you best because sure as shootin' there's a gun out there to fit you like a glove.
 
I would get the sidelever for a few reasons. Firstly it allows you to use a bipod which should not be underestimated. Secondly and most importantly, the only readily available sled operated rifles are both sidelevers, the high power RWS 54 (best in .22) and on the low power end, the used FWB 300 (.177). The reason the sled action matters so much is that it provides a built-in artillery hold eliminating the most challenging part of shooting springers. It doesn't hurt that both of these models are exceptionally accurate to start with.