How often are you commuting, what distance, and are you able to charge lights in work?
If not very often and not very far then buy cheap.
A few of us here ride 10+ miles to and from work every day and none of us run really cheap lights because they fill up with water and stop working with amazing regularity. Even when they don’t get waterlogged, it’s not a great feeling to be half way home and find that your main light has just sputtered out and you’ve got the darkest part of your ride to come. We have regular boring conversations about this subject, when yet another light has failed!
The Specialized Flashback rear light has become my go-to – it’s lasted about 2 years now. Front depends on what I grab but through the worst of the winter is normally a Lezyne 700lm. I’ve probably had it for about 3 years, and they don’t make that model anymore. They do various models with different outputs but they are over your budget. I’ll also put a couple of spares on the bike, but they will be cheap ones.
My wife bought me Planet X lights for Xmas 2 years ago. I don’t have them anymore – they are disposable if you use them every day.