Swapping MTB tires for more grip and less puncture, going tubeless: is it worth? I own a CUBE Acid MTB, which is mainly aimed at entry-level/XC riding, although (since this is the only bike I own righ now) I do ride it in somewhat more aggressive trails, almost enduro.

The bike has been running fine but I feel I could benefit from a new pair of tires, to increase grip/traction and to scare away most puncture and slipping thoughts, something that could withstand roots and non-plain terrain.

Also I'm still running tubes since my rims aren't tubeless-ready by default.

My bike has ETRTO 622x20 rims, with Schwalbe Smart Sam 2.25" front/back.

My understanding is that most rugged tires are 2.30" and up, while 2.25" tires are mostly a XC thing nowadays.

What tires could I mount on my bike? 

Is tubeless achievable on my setup?

If yes, I won't convert right away, so a tire that could work on both setups would be great.
I am reasonably sure you can set up the wheels on that bike to be tubeless if you want. The key thing to look for is whether the rim join is pinned or welded. If it is welded then you can probably set up the rim with tubeless for MTB tire pressures. 

I would only worry about "tubeless-ready" rims and tires if you are running smaller tires at higher pressures. For MTB riding one of the big advantages of tubeless is being able to run tires at very low pressures. You could easily go down to 20 psi. At that psi, I've had pretty good results converting to tubeless
with a wide variety of MTB tires. I definitely recommend going tubeless for any bike that sees a lot of dirt.

Looking at the spec of your bike I've found on the web, I'd guess 2.4 is about as big as you can go in terms of tire width and frame clearance. Without knowing more about where and how you ride, I can't make any specific tire recommendation. You can always put a tube in a tubeless or tubeless-ready tire. Ask around, I'm sure there is a local "magic" tire that riders in your area recommend. My general rules of thumb for MTB tires are : 


Wider is better, but there is a limit determined by the width of your rims.
It looks like your rims are 20mm wide, I'd stick with 2.3's(55-622 ertro) at most.  
Wider and knobbier on the front, smaller and less knobby on the back.
Drop the pressure in the tire until it's obviously too low, then slowly increase to find the right balance for where you ride. Ignore the PSI on the side of the tire.


For guidance on tire sizing and rim width, this is a good page. 
Sheldon Brown tire sizing In my experience, that chart is very conservative, you can push the limit but much of the benefit of tubeless disappears if the rim isn't wide enough to support the tire well. You'll just get too much squirm at low pressures.