In reply to TheFasting:
> Budget between 450 and 600 GBP
Are you willing to purchase some gear second hand? e.g. crampons or axes? You can save quite a bit. Are you buying in Norway?
> Rope: Mammut Finesse Dry 9.3. Pretty fat triple certified rope, so I can buy a cheaper half rope later to complete the set for alpine climbing instead of buying only one single and then two new half ropes. Or should I buy a cheap single first? A 300 GBP expense for two ropes later could be hard to manage.
A good choice, also consider the Serenity Dry 8.7mm if you want to consider weight. A very nice all round rope. 60m will certainly do for most things, as its dry you can use it for ice on single pitch/ non-convoluted routes without any worry. For easy alpine routes it shouldn't be much of an issue. So long as there are no long rappels. You may well end up with partners that have a set of half ropes anyway.
> Crampons: Grivel G14 seems like a good allrounder and it's modular so I think it last longer since I can change the parts as they wear. Does that make sense?
G14's are probably the most popular all round mountaineering crampon. What boots are you using them with? Are you getting step-in (cramp-o-matic) or strap (new-matic) versions? BD Cyborgs and Petzl Lynx can be worth looking at for price comparison.
A pair that can be converted to mono-point for ice and mixed is ideal, this will save you two front points for later. Second hand is well worth looking at. As you plan to do mountains/ alpine routes don't pay too much attention to dedicated monopoint crampons as these are not the best on hard snow and have pretty poor breaking downhill.
> Quickdraws: Camp Nano 6 pack set x 2 and one longer quickdraw for rethreading and cleaning. Do I need more? Different sizes?
Is this a QD pack or just the carabiners? QD packs are a good way of getting lots of carabiners, but perhaps consider building your own? For Trad, ice and alpine lightweight and with a good/wide gate opening is the most ideal. Especially if gloves are used and you have a thick rope. You can also build QDs with cheap 30cm dyneema slings thus they are all extendable and highly versatile. Ideally you want about 10 quickdraws in total, ideally 12.
My next quickdraw set will be built from Mammut Wall Light (23g) carabiners for gear/ice screw end, Mammut Wall (27g) carabiners for rope end with 30/60cm Edelrid 8mm dyneema slings (8/18g). This is the lightest set up, with the widest gate opening and decent size of carabiner I have come across from weighmyrack.
> Ice axes: Not sure if I can afford both but I can borrow these from my club. I'm thinking about 2 Petzl Quarks at the moment. Will be used for waterfall WI4-5 for toproping at first, then general technical alpine climbs.
Anything with good knuckle clearance will do. Quarks are a great all-rounder choice but are not the best for steep or featured ice. They will however serve you perfectly for long alpine routes and easier multi-pitch ice. I would say use any weekends you have on ice to try as many tools as you can. Rjukan is good for this at the ice festival. When you swing enough, you will get a really good idea of what you prefer/ want.
DMM Apex, BD Vipers are also worth considering for this type of axe. I personally use BD Fusions for everything and have Petzl Sum'tecs for anything less technical. Everyone I know who started out with technical alpine axes like Quarks, Flys, Vipers etc have sold them for Nomics or palmed them off to unwilling girlfriends.