I've never played either but now only have my netbook as a gaming platform... I always heard they were good and figure they probably have decent offline considering thier dates. Will I lose much just starting 2?
They don't have a decent offline! They have awesome offline! Don't forget that this games appear when there wasn't much of hi speed internet. They are both a little bit different so if you start with second you can play fist later.
I spent epic days with a friend playing through Diablo 1 in LAN and on my own on PSX. Totally worth it imo, but it shows it's age. Just like Diablo 2, the resolution limit of 800x600 is rather annoying on LCD monitors (looks like shit, there is a neat resolution hack though for diablo 2). IIRC the intro of D2 explains what happened in D1, so you won't miss much of the story.
I'm just about to play through Diablo 1. It's a way shorter game than Diablo 2. Just one dungeon with 16 levels. So yes, I would say start with Diablo 1, it won't take you long to beat it anyway and it's good fun.