I’m assuming that you’re currently doing your level 2?
If so, you’d be best off sticking with whichever brand they are using at college as the teaching materials will be written to match that brand.
For instance, when choosing the correct strength of developer to go a shade darker, you might be told to use Goldwell Developer 3% but if you’d bought Wella Koleston Perfect, it doesn’t have a 3% but uses 6% instead. Looking at it the other way around, using 6% with Goldwell will lift the natural colour too much and the end result would be wrong.
Another difference is with the tones. Some brands use letters to denote tone and others use numbers so G=Gold in Goldwell or /3 in Wella. Goldwell is a German brand so they use K for Copper, not C.
In Wella, /1 is Ash but it’s a grey ash so should not be used as a neutralising tone but in TiGi, /1 is a blue based Ash and its different again in Schwarzkopf as their /1 tone is a green Ash and /2 is their blue Ash.
More important than a shade chart is the Professional Colour Handbook. Most of them can be downloaded and you’ll usually find them on the section of the brand’s website designed for qualified professionals.
Level 2 colouring is usually covering the basics and more about simple colour choices and practising your application technique rather than in-depth colour training.
You won’t be taught much about colour correction on level 2 and some students finish level 2 thinking colouring is about choosing a pretty colour from a chart and applying it but it’s a lot more complex than that. Having the Brand’s handbook will give you their basic colour chart but a lot more information besides, so it’s well worth downloading.
