I've spent a fair amount of time in that area climbing. The main destination is Chamonix, but there are others. You basically have a choice: bolted limestone midsize mountains with sport routes of 1-10 pitches, or the granite massif of Mont Blanc / Chamonix. If you go to Cham you can easily access some limestone routes. Also, on the opposite side of the Chamonix valley are a third massif, the Aiguilles Rouges, which have some decent gneiss, again bolted.
It's worth maybe even ordering a guidebook in advance, but don't feel obliged to.
The Potard guide mentioned is pretty good - and in English. Mostly though it just covers little 'jardins d'escalade' or 'ecoles d'escalade' which are where you go to learn to climb (bolted crags 1p etc), though it covers Barberine which has some lovely multipitch routes that go at 5.9 to 5.11a.
For some alpine routes of wonderful quality, look for Michel Piola's guide Mont Blanc Range Topo Guide (Vol. 1) which is also found in English. This covers rock routes only, trad and adventure-bolted climbs (they bolt a lot, but bring a rack and alpine gear), mostly on the granite massif, and some routes in the Aiguilles Rouges.
The classic Rebufffat guide '100 Most Beautiful Routes of the Mont-Blanc Massif' has been republished in Britain, you might be able to find it. Covers older style alpine routes from snow plod up to crazy-hard. Lovely book.
So those cover Chamonix. If you're going there, why do 1-pitch modest clipups when you can do the great big climbs? I'd get the Piola guide and have a ball. You won't get in over your head, don't worry.
For going elsewhere, unless you want to do glacier plods, you're looking at limestone, and all your guidebooks will be in French. Michel Piola has some lovely topo guides (Calcaire en Folie vols 1 & 2) which are easy enough to figure out if you don't parlez francais.
BTW, if you do speak French, you have a few other guidebook options, but stick to the ones mentioned above in Chamonix. The one other one worth looking at covers the Aiguilles Rouges only.
If you want to do some great routes in the 5.4-5.7 range (I'm guessing?) I'd suggest trying to hit the granite routes if the weather allows. I assume you can cross very easy glaciers (nothing serious, maybe a steep bit at the base, but low crevasse danger).
GRANITE TRAD ROUTES (ALL NEAR CHAMONIX)
Aiguille de l'M - smallest of the Aiguilles de Chamonix, NNE Ridge is a classic 5.7. A good starter route for the mountains, long enough to take a day, not too long to get over your head. Crux is a slick 5.6 move, the 5.7 is easy!
Pyramide du Tacul - another classic 5.7 you'll find, glacier approach, spectacular setting. Mostly 5.4ish.
Papillons ridge on the Peigne - one 5.7 you can aid, the rest is awesome 5.4-5.6. Heading for the summit makes for a long day for the 5.6 leader, but doing the normal route on the Peigne is some nice easy -grade mountaineering that will test your routefinding, so doing the normal route one day and the Papillons to where it hits the normal route on the next day could be nice.
Sonam or Rhododindons - good excuses to visit the lovely Envers des Aiguilles hut, an awesome hike (ladders!) and these are two moderate (but Sonam is long) routes in the Envers area. This place is full of 15-25 pitch 5.10 climbs - and 5 star climbs at that. Also from the Envers you can do some ultra-classic alpine routes (5.6 max) that are long days (I don't know how much mountaineering experience you have so I won't recommend any, you'll find them)
Lots to choose from. The Dent du Geant, for example. Acclimatize first. 13,000'. Table de Roc route on the Tour is one I always wanted to do. Or do Mt Blanc - it's a lovely peak no matter which way you snow-plod up it.
MULTIPITCH ROUTES IN THE AIGUILLES ROUGES (GNEISS)
Chapelle de la Gliere - one 5.7 move, a long but fast climb (14 pitches half day?!?!), trad
Index - 3 or 4 pitches, 5.5-5.6, trad
Frison-Roche - 6 pitches, ever done a bolted crack climb? 5.9+ but have a go
the wall at the top of the cable car with Asia etc - some classic moderates
All bolted. I'm not sure what there is below 5.8 but there are plenty of 5.8 or 5.9 4-5 pitch routes all over the place. there is a 17-pitch 5.7, bolted, NW of Cham that's not in a guidebook. If real mountaineering seems too ambitious for you, try to find that. It was in a magazine somewhere, ask at the OHM (see below).
Note: The Office de Haute Montagne (OHM) is in Chamonix and an incredible resource. They have all the guidebooks etc., and a staff on hand who give advice, and notebooks for route descriptions, notebooks for people looking for partners, keep up to date on route conditions, etc. They speak English. ohm-chamonix.com
In Chamonix, you don't have to camp (and thus don't bring all that stuff on the plane). If you have $, you can stay at huts up in the mountains (not too expensive, $20-$30 depending on FX rate and particular hut) instead of bivy. I would do this at least once, for the experience. (e.g. you are placed in a bunkroom based on the route you plan to climb - and thus the hour you are awakened!) There are campsites in Cham, pay sites. Worth checking out for a little extra dosh are the guesthouses "gites" - ask the tourist office about these - a step below a hotel, kind of like a hostel, tend to be full of climbers and hikers. Some nice ones include the Tupilak if you have a car - it has an indoor bouldering wall, La Tapia (Sophie makes it feel like a home instead of a YMCA).
Hope that's a helpful start. Have an awesome time.