Anything will be better than nothing. Mechanics gloves from any home improvement/hardware store will offer good protection for climbing, working etc. However, the all leather work or gardening gloves will be better, IMO. I prefer the deer-skin ones since they're more supple, break in quicker, and aid dexterity. The only downside to all leather gloves is when they get wet. Take forever to dry out, and crappy ones don't work as well when soaked. The synthetic gloves put up with being soaked better, and work better (usually) for fine motor tasks.
However, if you anticipate dealing with fire or any hot objects, you're better off with simple, all leather gloves, IMO. All the synthetic material gloves will melt to your skin, unless they're specifically fire-resistant, and those are more expensive. While you may not be in burning buildings, even just working around a campfire can cause problems.
I don't know about the cut resistant gloves, since I don't own any. I've been happy with the leather work gloves for cut-resistance, when gardening and camping.
The importance of gloves just can't be over-stated, especially in emergency situations. Along with boots, a hat, and eye-protection, they're essential, IMO.