I assume that you are targeting ball point or roller ball pens - I'm a fountain pen user myself, and acknowledge that to be a bit of an oddity. But if you are thinking fountain pens, the issue in most cases is that the nibs that come with kit pens often (generally) need tuning. You can learn to tune nibs, but you will need some supplies (sheet brass for 'flossing' tines, and brown paper bag for smoothing tips). And you will need some time and at least one pen to practice on - tuning is a skill that takes time to learn. I've found that the medium nib kit fountain pens in my collection write reasonably well, but I did have a problem with an El Grande with a fine nib.
So the key issue in writability with ball point and roller ball pens is not the kit itself, but rather the refill. Most kits come with generic refills that are pretty crappy, and the best way to make them write better is to replace the generic refill with something of quality. Keep in mind that in most cases, the cost of the entire kit isn't greatly different from the cost of a quality refill, so the 'original equipment' is likely to be pretty lousy. So if the kit uses a generic Cross clone, replace it with genuine Cross. Or if it uses a Parker style refill, replace it with a real Parker refill. You should be able to find both Cross and Parker refills at Office Max or Staples.
There are other brands that are almost as good as Cross and Parker, but make sure that you are getting the real, branded product and not a no-name ripoff. Monteverde and Schmidt refills have a good reputation.