Hi and welcome to the forum.
You shouldn't have a problem finding a good 3.0 manual within your budget.
But bear in mind there was a facelift in early 2006 and you might struggle to find a facelift model, unless you don't mind it being a bit leggy.
The most significant difference was the change of engines.
Pre-facelifts are designated 3.0i and use the M54 engine with 231 bhp.
Facelifts are designated 3.0Si and use the N52 engine with 265 bhp.
I think the later engine suits the Z4 better - it revs higher and produces more power! But it has a couple of irritating foibles - there is no dipstick, you check engine oil level via a sensor by pressing a button on the dash. And it has an electric water pump, so when it fails it tends to just stop and wherever you buy a replacement it will be the wrong side of £200.
There are usually a few cars for sale on here, and they're more likely to have had an enthusiast owner so it's not a bad place to start.
Anyway good luck finding the right one for you.

And when you have don't forget we like photos!
ETA I just read your post on "bbrys" thread - you could always consider a facelift 2.5Si. It's got the newer N52 engine just in 2.5 litre form and 218 bhp so not much behind the older 3.0i - just make sure you avoid the facelift 2.5i as it's got 177 bhp IIRC!