As Douglas Cole pointed out with our fighters in Swords & Wizardry, there aren't a lot of options to choose from. As a result, we don't spend a lot of time trying to figure out what to do. Hit, not hit . . . what to hit what, who to hit. Not all that much turn to turn to decide about.
In GURPS, though, combat options are what it's all about. There are many things you can do, if only because combat is less abstracted and there are rules covering such a broad variety of options. You can try anything, and it sometimes feels like you should therefore try everything. Worrying about what option is right for right now can lead to that dreaded condition, analysis-paralysis. You can get so overwhelmed by choosing between things you can do that you don't just do stuff and get on with the fun.
Too Much to Choose From?
If you have a character with a sword, a shield, and pretty good brawling and grappling skills, you can find yourself thinking - you can cut, stab, bash, shield rush, slam, kick, pummel with the hilt. If you do any of those, you may need to choose a hit location. Any of those could be All-Out, Committed, a normal Attack, a Defensive Attack. Should you attack normally, or Telegraphic Attack, or Deceptive Attack; and what about Rapid Strike or Dual-Weapon Attack? Or you could feint, beat, try a ruse, or even just All-Out Defend. And next turn, it starts again.
So what to do?
Limit Your Own Options
Seems like a bad idea, but it's not. Look at that list above - are all of those solid moves in nearly all cases?
Narrow it down.
Look at your skill, possibly at this analysis too, and decide if you should generally attack, Telegraphic Attack, or Deceptive Attack. If your skill is too low to reliably hit without Telegraphic Attack, do that. If you can take a Deceptive Attack and still hit most of the time, do that.
Make a basic decision and stick to that, most of the time.
Look at your weapon.
In fact, if you're just getting used to GURPS, don't go for the most versatile weapon. A simple cut-and-thrust sword is good - save the tricked out-dueling halberds for another time. Don't worry too much about slams and kicking and grapples just yet, because generally if you've got a weapon it is more productive to use it. Be aware they are out there as options, and bust them out of you need them. But don't go out of your way to give yourself too many options at first.
Limit Your Targets
Pick a couple of targets that suit your weapon, either for a baseline move or as a potential kill shot. You don't need to have a mastery of all possible outcomes with your weapon - it's sufficient if you have a pretty good shot you know will work, and fall back on that.
Find A Default Option
Most of the time, just using your highest-base-damage attack, without modifiers, aiming at the Torso, is all you need to get through most fights.
The Trademark Move in GURPS is a heck of a speed-friendly perk. Spend 1 point, outline a specific combination (all options chosen ahead of time), and get a +1 when you do that specific move. It's a nice little reward for speeding yourself up. It cuts the decision time down, because you know if you stick with your pre-decided move, you're more likely to hit.
Consider a backup, even if you can't or don't buy a Trademark Move for it. Just outline what you want to do and mark it down.
In either case, write it down on your sheet for quick reference.
Don't Adjust On The Fly
Stick with what you're doing until you've got some downtime to think about your choices. Sure, when the chips are down and you need to bust out a special move - do it. But save the analysis and worry for it really matters. Do it when you've got downtime, or when it's a nailbiter of a fight to the finish. Don't drag out fights by getting too wrapped up in all the stuff you can do, and just stick with a few moves that will win you most of your fights.
Those are just a few things you can do to make sure you're not overwhelmed by your options. GURPS gives you a lot of substantial, significant options to choose from. Pick a few, run with those, and adjust as you get more familiar with what's on the table. Odds are, though, you'll find you'll return to the basics over and over. I've been playing GURPS since Man-to-Man and most of the time my characters just whack the body with a high-damage attack.