I have been looking into how strong of a bow would be required to bow hunt moose. I haven't been able to find a specific number as to how many fps you should be shooting to safely hunt moose.
With the bow it is not the speed of the arrow but the power it is packing. I think the general speed is around 300 fps (90 m/s). There are some compound bows that can shoot faster with thin diameter arrows.
Usually 55 lbs draw is enough to kill any large game. I shoot a 65 lb take down recurve when I train. Than I switch my bow limbs for 50 when I hunt (also train with it but not as much as with the 65).
If you take look at Hoyt website they have hunters taking down buffaloes with 50 lbs bows.
Also a lot depends on your arrow head and the diameter for the arrow. Thinner diameter penetrates deeper. Quality arrow head will slice up the heart so the animal bleeds out in matter of seconds.
Also it depends what you prefer to shoot. Some guys like longbows because of the feel and raw power. But it takes a long time to master.
Most people shoot recurves because they are easy to start with and are affordable. Also the bow generally does not vibrate as much as a longbow.
Than you have compound bows. I don't like them very much. To much tech and at some point you just better of with a rifle IMHO.
To safely hunt anything you have to know your game. If you go hunting moose that is pissed off at you; well you are asking to have meeting with the reaper.
When hunting with a rifle, it's the energy of the bullet that matters. With an arrow, it's all about blood loss. The 'power' matters, but only insofar as it is a factor in creating blood loss. Ideally, you want a through-and-through so the arrow is out of the animal's body and does not block blood flow. What's necessary wrt fps for an arrow to kill a moose? Search on Fred Bear and moose hunting. I doubt that any of his arrows were over 200 fps.
A high-speed arrow, say, high 200s fps or higher, is more forgiving with respect to judging distance, which is often a difficult skill to master. It's more forgiving because a fast arrow has less arc. If you think it's 50 yards and it's only 25, the slow arrow might arc out of the ideal kill zone and the fast arrow might still be in the zone.
You need to meet the minimum requirement in the hunting regulations. A crossbow has a different minimum poundage then a recurve for example. Go as high a poundage without sacrificing accuracy.