I used my T2i for video only.
Among other lenses, I also have a L series Canon 70-200 mm F4 zoom = $700. I brought a USED, CHEAP, OFF BRAND 80-200 mm zoom = $75 a few weeks ago. The Canon is better, but NOT by a mile.
Video don't need sharp lenses as much as still photography do. Not a doubt, better lenses look better. But I paid 10 times more for 10% better image quality at wide open (F4) otherwise not much difference after F8.
That being said, the built quality and user experience form the Canon L series lenses is TOP NOTCH! Hands down!
Looks like you appreciate good quality, then go for Canon L series. Always rent first, then slowly built up your collection.
At the start go rent some lenses. After enough field experience then decide what to buy/keep/sell.
For example I learned that the EF 28-135 has good photography quality. So I paid $25 to rent one for a paid shoot. Afterwards I learned from real field experience that the image quality is very good. I can mixed it with footages from the Canon L series lenses. But the variable max aperture is a NO NO NO for video - like everything goes a step darker when you zoom in and when you zoom out everything goes brighter again. And also the zoom ring is not as smooth as the L series. This is another deal breaker cause I need silky smooth zooming when shooting the show.
See sometimes you need to use it to know how it suits you.
Color difference in lenses is a non issue cause you can always CC your footage. But of cause better lenses are always better. Just how much you want to paid for "better."
Lenses I use with my T2i (other then my HVxxs):
Canon 18-55 mm kit lenses. Good image quality but NOT for low light. Built is CHEAP. Really low price. I just use it for the wide end.
Canon 50mm F1.8, Good image quality. AF is super fast. Built is CHEAP. Really low price is good.
Pentax 50 mm F1.4. All metal, good image quality for low light. Focusing is a joy, smooth like butter. Cheap, like $50.
Canon 70-200 mm F4 (non IS), use on tripod all the time. Built is TOP NOTCH!
Pentax 135 mm F2.5(m42) really good image quality for low light.
Off brand "Albinar" 80-200 mm F3.5. All Metal, Built like a tank. I think this guy WILL out live me for sure. Good image quality except at wide open like F3.5. Step down to F5.6 then it's no problem. Not a huge different in outdoor shoots when compare to the Canon L series, because video is really low res by comparison to still photography.