Would spreading around my skill points at level up be a bad idea?
Probably, especially if you do that 1 point per skill thing. There are a bunch of skills you're probably not even using much. For example, chances are you're relying on one combat skill. So why waste points on something you're not really using?
Would focusing solely on my tag skills until they are 100 be a better way to go?
Possibly.
Depending on how you want to play, your best bet is to focus on a few skills and once they get to an acceptable level, work on others. With the build I'm playing now, I have to be really careful how I distribute my points to have everything where I want it for the levels in which I need it. The big thing for me is to stay ahead of the Speech curve, so I never have to worry about failing a check. But I've also had to put a lot into Repair and Survival for certain perks (Travel Light, Light Touch, Hand Loader). Additionally, Locks are important, particularly since I want to get Lucky ASAP. Once I get to Repair 70, I'll be focusing more on Barter for Pack Rat. Of course, I can't neglect Sneak, so I can get Silent Running. On top of all that, there's a lot of checks that involve Science, and some Medicine, so I'm keeping those in mind, too. I'm not even bothering with combat skills as I have too much else on my plate right now.
As you can see, it's possible to have a lot to consider, depending on your build, and it can change at various levels. Your best bet is to think ahead (say, to level 20) as to what you want your character to be, and plan accordingly.