>For pretty much most other household items I have found prices to be comparable or even better at a local retailer. I went to buy a bicycle lock on Amazon this weekend and they had the brand I wanted in a range of 36 - 80 USD depending on model. Local retailer had the same brand in the 25-40 USD range. I have had similar experiences with a lot of different products in the same bucket of "general stuff." The pricing is not always better.
Anything that is a major brand or common product will always be cheaper online by very definition of not having to pay for a storefront, if you can't find it cheaper online then you simply aren't looking in the right place or manner.
A lot of people swear by Kryptonite locks. They have a lot of selections for as little as $25 on Amazon.
Website https://www.kryptonitelock.com/en/locks-landing/product-details-bicycle.html
U-lock with 4' cable https://www.amazon.com/Kryptonite-KryptoLok-Bicycle-Lock-Cable/dp/B005YPK8G2/ref=sr_1_1?ie=UTF8&qid=1505834415&sr=8-1&keywords=kryptonite+bike+locks
For your size and needs you'll be able to find a nice used bike without too much hassle for sure. Rather than tell you exactly what type of bike you need, however, here's some general ideas you'll want to keep in mind:
Sizing
The nice thing about used bikes (such as you find on CraigsList) is that they're plentiful and cheap. The downside is that personal sellers rarely know how to properly measure their bike, and certainly don't know how to tell you if the bike fits you properly. This is a big deal because bike sizing is a HUGE component of your health and happiness. Before you look at used bikes, go to your Local Bike Shop (LBS) or bike co-op and talk with them about bike sizing and fitting, and what it is you personally should be looking for. Make sure you sit on a few bikes to get a first hand feel for too small, too large, and just right. Know what a "standover test" is, and how to perform one on your own. I've seen plenty of people rev themselves up for bike commuting only to buy a bike that doesn't fit their body at all, and a month later when all they know about riding is the pain, they drop the whole idea.
Styles
Different people like to commute different ways. Already a couple people in this thread have suggested you get a fixie. Nothing against fixies, I love them myself, but they work well for certain people in certain terrains. For instance, I live in a city with steep hills. There is no way a fixie can accommodate the range of vertical change here. Riding that sort of bike here means choosing it in spite of the geography. Likewise, in the flat midwest US a 3x10 set of gears is pretty superfluous, so ditch the weight and get a single speed. Make sure you identify the needs for where you're at. Hills? Get gears. Wet weather? Make sure it has fender mounts and pitch some money for fenders. Are you carrying 30 pounds of text books? Make sure it has a rack mount and buy some panniers, because heavy backpacks suck. Your goal right now is not to find the coolest bike. It's to find the bike that makes you happiest to get back on and keep riding it, and you won't get that if the bike doesn't fulfill your needs.
Accessories
Be prepared to want (and need) some accessories. These will cost money, and they will be well worth the investment. Like, fundamentally, a bike lock. Just like the bike, most of these accessories are worth their cost (to a point). If you're worried about bike theft on campus or around town, don't get a cable lock. Buy a U-lock. Something like this is enormously better than a cable lock without breaking the bank. And that's pretty much how any good accessory will go. The cheapest stuff is crap, but if you go just a little higher in price things get much better much faster.
On the other hand, there's also a lot of ways to cut corners and save on accessories that will really make your commuting life more enjoyable. Personally, I buy my gloves and emergency rain gear from Home Depot. Because I'm cheap and that gear doesn't need to be fancy bike stuff. It just needs to get me home in a pinch. Having decent gear is nice, but don't let someone swill you on needing bike specific stuff when non-bike stuff will do just as well.
Best of luck starting the commute!
Here you go, less than 20 euros.
I'd only use 2 locks, 1 U and 1 cable for accessories.