I've just taken delivery of a new Canon 7D (body only) for work. I've been recommended three lenses by the supplier who know what I'm going to be using the camera for:

70-200mm F/2.8L
50mm F/1.2L prime lens
15-85mm F/3.5-5.56

I'm going to be using it mostly for shooting videos in the mountains (in all weather types) in the UK, indoor/outdoor and under studio lights. I know that the lenses are just as important as the camera (or more important depending on what you have) but there seems to be a huge range in pricing for the range I've been recommended.

Unfortunately, the company I work for has a tight budget, but I don't want to get something cheaper and then find it's not going to get the best results.

I shoot a wide range of stuff, from a static shot of presenters in a podcast, to tracking someone skiing past me or with me skiing with them.

Could I ditch the prime lens and make do with the 70-200 and the 15-85?

Someone else recommended the Canon 50mm f1.8 which they said although a bit plasticy produced great results. Plus the Sigma 10-20mm F3.5 EX DC HSM as another option.

I haven't shot video with a DSLR before so please excuse my ignorance!

My budget is around £1500 (US$2300)

Thanks!