Im not sure i follow everything described however the number one thing here is that it is extremely difficult to bud a machine capable of handling steel well and being a cost effective wood router. To put it another way you will not be able to machine steel even like a light weight milling machine (Bridgeport for example).
Im a bit confused as to which axis is which in your description however unless this machine is huge i generally see ball leadscrews as the most cost effective axis motion solution. Like wise you will want to use linear rails on all three axis. Done right it is fairly easy to get a machine that can do wood, some composites and aluminum well. To machine steel even modestly requires a very stiff machine.
By the way machining steel means different things to different people. If you are thinking engraving size tools you might get acceptable results. You will not get a router to replace a general purpode milling machine. At least not for 2,000 Euros.