In reply to Jshaw04:
So I think you should aim for doing some Alpine hut to hut treks, or base yourself somewhere where you can easily get high then back to where you are staying. Some of the passes are over 3000m. Find a quiet area the Alps cover a large area, theres loads of places you can go and not trip over countless guides and others climbing.
By trekking/hiking there you'll understand more the weather patterns and the scale of the mountains. Scotland is good preparation but expect to be ascending a hard gradient for much, much longer and above 1500m altitude does come into play. Dont worry about the height of any mountain you ascend they all make the uk ones (great and fantastic though they are) feel like hills and it's about you having a good experience not about a checklist.
If you do go to a summit it's really important to get up really early so you can be down off the top well before lunch. There are myriad reasons for this and you should know them all. Check the weather as always but you should be used to this as you must do this in Scotland. For glacier travel and most summits, as others have said you must be able to do crevasse rescue and have the right equipment to do so. Crampon obviously but ice screws as well, ropes, harnesses, protection and not forgetting the most important thing a helmet.
Travel light is for professionals just take what you need the more you do the more you know what you can ditch. Dont drink untreated water (take tablets or filtration) often carries shigella bacteria my mate did last year and was seriously Ill for days.
I still find the scale of the alps pretty intimidating and it should be said that they are dangerous. I had a small slide last year, outcome would not have been fatal had I not self arrested but I bounced off a rock and sliced my leg open. Luckily I took a decent first aid kit to pull it together (steri strips are great) until I got back down to medical assistance 36 hours later.
And I wish I was 21 I have trekked and hiked all my life but didn't start mountaineering till my mid 40s so you have loads of time to get the skill set you need! And yes get really fit you'll enjoy it more!
Hope that helps!