Hey guys, for an enterprise wide deployment, what will you suggest and why among - Red Hat Linux, Suse Linux and Ubuntu Linux, also, do you think, we can negotiate the support pricing down?

deployment of what, where, why?

It's impossible to say anything without a lot more information than what you've given.
If it's a collection of servers Ubuntu would be less appropriate for example than the others.
If it's workstations it may be the best choice.
If your people (both users and especially admins) have no Linux experience any Linux may well be a poor decision.

If you're a cheapskate and don't want to pay for support it's going to hurt you down the road in higher incident management cost (having to call expensive hotlines with per-call charges you didn't think were worth the money covering in your support contract).