I have a Lenovo Think Pad with which I'm well pleased. Originally these were made by IBM. I don't do any graphics work, don't upload anything so it's pretty much used for writing, reading news, watching movies on Netflix. I'm told it has enormous capacity-and it well may, I'm not a technie, I'm a Physicie, and I'm old so all I can do is say I'm well satisfied. It's very light weight, indestructible, at least to date. It wasn't particularly inexpensive but it wasn't tremendously expensive. Having given you little to no help, I'll sign off.
I just heard on the news that the Vaio's have a major battery malfunction and over heat......could explode and/or damage your laptop. So I would cross those off the list for now.
This particular model is not available on the site now but the next one up is. Also, mine is the Dell XPS (#1 in the youtube vid posted above) and it DOES rock!!!!
Life's too short to miss an opportunity to show your love and affection!
Edit: I'm stupid and read you wanted it for university. Fixed it.
Make sure you know what specifications you want for what you need. For example, heavy gaming will warrent several cores, a game card, ram, etc. For school you'll need much less. The laptop Ccrox posted I think would be a good 'general' laptop, and that's the price you should expect for a laptop like that.
Knowing the specifications you'll need it important, so you don't pointlessly spend more money than you need.
As for what brand of laptop, I've had both Acer and Toshiba, and vastly prefer the Toshiba. But I actually am not bothered by the brand much.
EDIT: if you can try not to get a keyboard like this. I found it almost impossible to clean on my old laptop, and I spent hours on it. An unbelievable amount of filth just falls in through the keys and you need to take every key off to clean it (which can break them), and even then sometimes it's tangled up and just not fun.