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I normally recommend the fast prime set for all cinematographers and a lens kit to fill any missing focal lengths.

50mm f/1.4
28mm f/1.8
35mm f/2
85mm f/1.8
all these together will run you a bit over 1.5k (euro)

this however is far from what you want if you're shoting live events. I know what a headache they can be if you are not prepared with the proper equipment

Canon offer a 17-55mm f/2.8 IS USM which I was looking to buy to replace the kind lens, unfortunatly this is a EF-S but at least it's well around your budget

If you want a lens that is considered fast do not look at anything with a value higher than f/2.8

Also you need to decide what you need it for specifically, how you do this is to film with the kit lens, where is fails is where you need to improve by upgrade, if it works fine you dont need to upgrade and kit lenses dont shot any different in video over l series lenses (in photography its another story)

I hear sigma also make some good lenses but I can't recommend something I do not own. My friend owns a sigma and his only con is the focus ring is very poor

Just convince me that higher bitrate results in noticeable better quality. But not with a ton of text.

The best video I always use to convince people about the use of CBR

Not my own but it's great for showing the differences changing the bitrate can have on footage