Hi what matters with your laptop is the spec [i.e. good hard disk size [at least 500GB], RAM capacity [min 8 GB], reasonably good graphics card, quite fast CPU [perhaps not the very latest ones to save money, but can still be equally good e.g. an i5 quad core one of perhaps 5th or 6th generation]. If your budget is tight, I would search for the specs above rather than concentrate too much on the make or model. In fact, if you go for a good refurbished machine from a firm with great feedback online, you can pick up a super bargain with slightly older tech, which would serve your purpose just as adequately as going for a brand new machine with a "renowned" name.
Some sellers will throw in MS Office and/or some other apps into the package [they purchase multiple licenses in bulk so can afford it] - try and get Office 2013 or later. If you are planning to become a teacher, MS Powerpoint and/or Adobe Illustrator might come in handy.
If the laptop starts slowing down after a couple of years, t is quite easy to just add some RAM to quickly and cheaply speed it up. Most unis will have a tech help desk, where you can obtain advice and help.
Best wishes!
M