Okay, I've been going over this many times in my head, wondering just how awesome the concept would be.
 
I believe that Surfer's fighting abilities are somewhat limited to basic pugilism, and coupled with his powers, he's fairly formidable. But what if he was trained through martial arts? Would having an array of fighting talents make Surfer a better character, or would that warp his general perspective as a character?
 
I mean, if he combined his newly found martial arts abilities with his powers, do you think he'd be able to fend off greater threats?

TBH I don't think it would. It would actually make him look a little strange to me. 
Although Silver Surfer is Class 100+ (able to further augment his strength with the power Cosmic), he is one of the few heavy hitter who normally does not have to resolve his conflicts with physical confrontation but normally with energy manipulation such as Reality Warping, Energy blasts, Force Fields etc. 
Most of the problems that Surfer encounters are very unique to those compared to Daredevil or Wolverine who need to employ such fighting techniques in order to overpower their opponents. 
Silver Surfer usually doesn't go up against an enemy that would give him so much trouble that advanced h2h combat techniques would need to be used or be the deciding factor. 
I couldn't imagine seeing Surfer karate kick Thanos for example ;p 
I like Surfer how he is and his current power set and fighting style. Attempting to shift his character to a more physical combatant would be somewhat awkward. 

Not much training, without his powers he was doing impressive stuff with his body and taking out army men and a pack of mutant wolves by himself. He's a real daredevil without his powers in terms of H2H and is pretty decent. 

@Kallarkz said:

TBH I don't think it would. It would actually make him look a little strange to me. Although Silver Surfer is Class 100+ (able to further augment his strength with the power Cosmic), he is one of the few heavy hitter who normally does not have to resolve his conflicts with physical confrontation but normally with energy manipulation such as Reality Warping, Energy blasts, Force Fields etc. Most of the problems that Surfer encounters are very unique to those compared to Daredevil or Wolverine who need to employ such fighting techniques in order to overpower their opponents. Silver Surfer usually doesn't go up against an enemy that would give him so much trouble that advanced h2h combat techniques would need to be used or be the deciding factor. I couldn't imagine seeing Surfer karate kick Thanos for example ;p I like Surfer how he is and his current power set and fighting style. Attempting to shift his character to a more physical combatant would be somewhat awkward.

Agreed entirely. If anything, the fact that the Surfer is not an uber skilled H2H combatant, perhaps, is his weakness (particularly since he really has no known weaknesses). Also right about the Surfer's fighting style being one of long distance strikes, moving at crazy speeds, as opposed to "getting his hands dirty" with physical combat. As you mentioned, he is more than capable. An early issue of the Fantastic Four demonstrates the Surfer's ability to amp his strength to crazy levels (issue #55 I believe). And there is no indication in that issue that that was his upper limit. His fight against Beta Ray Bill, who is roughly the equal of Thor (who has matched a pissed off Hulk in strength multiple times...), is an indication that Surfer doesn't really need much in the way of fighting skill. His power is already overwhelming without it.