The majority of complaints about Touchwiz lagging come from owners of older samsung devices who havent even tried the S6. My previous Samsung was an S5 and THAT hung, lagged, crashed and whatnot. The S6 however doesnt lag even with multitasking (and I mean even with actual Split Screen multitasking)
You might have a few niggles every now and then but apart from that the S6 is smooth. I initially did have a bit of lag but an update sorted that out.
How does S6 work in texting, emailing, web browsing and listening the music (in multitasting mode)?
I have no Idea about texting because I use whatsapp which runs smooth.
Email works great (both inbuilt email and gmail and outlook; I use both Outlook and Gmail)
Web browsing is as good on Chrome as it is on Safari (I do have an Iphone an i pad too; I personally find Safari annoying) I dont use the Inbuilt browser much because I prefer having integration with Chrome on my Laptop
Music works great on Google play music which I use and also on the inbuilt music player.
Using all of these together is not going to slow down your phone

It will be as fast as the newer iphones and a lot faster than the 5S.
If you're shopping for a Galaxy, consider waiting for the S7 (launch event this Feb 21st) Even if you dont want the S7, the S6 will be sold at a cheaper price.