To quote the Rules......
If a character has no level in a skill, then he is untrained and will suffer a –3 Dice Modifier when trying to use that skill.
If a character has zero level in a skill (Skill 0), then he is competent in using that skill, but has little experience. He does not get any bonus from his skill ranks when using that skill but at least he avoids the penalty for being untrained.
So, in essence, a skill level 0 means you don't suffer a -3 DM on your roll.
In your example, a Computer-0 means that they can use a computer, and possibly even use (or write) basic macros, for instance.
Untrained would mean that they can log into the internet & check their facebook, but that is about it.
Yes, in character generation, both characters would go to skill level 1.
For my usage, I'd go for level 0 in cascade skills i.e., if I am an engineer, I'd want Mechanical-0, Computer-0, and Electronics-0 as a minimum. This way, if something goes wrong in Engineering, I don't want to be rolling with a -3 DM that untrained brings to the table.
I also don't want to waste skill slots. In my CE Universe (Call of MegaCepheus Engine), characters have the same skill level restrictions as in MT (skill levels can not exceed INT + EDU).
Real life example......
The unit I deployed with for Joint Endeavor was an officer heavy notational unit that was only issued 9mm pistols. Up to that point, I had never fired one, being one of the rifle armed enlisted swine.
I was given 5 minutes of instruction literally as I was preparing to go to the firing line. A quick how to load the magazine, set the site picture, and charge the weapon. That's it. I already knew how to use a site picture, so it was simply applying what I knew to the new weapon. I promptly qualified expert (since I had no bad habits to unlearn) and did so for the rest of my career.
Auto-pistol-0.
Had I not gotten that 5 minutes of instruction, I wouldn't have been able to qualify, because I certainly wouldn't have been able to swap magazines in the allotted time, much less how to hold the weapon to get a proper site picture.
Untrained (-3 DM)
Hope that helped.