Hi amine2,
To do this in they way that you want you need to think backwards, from the printer, to decide it's spec first!. decide the printing window x,y in mm and then height of max printed object. once you know that you can put down carriage design.
Being new to the subject I would recommend that you simply get one axis working first on a 3 axis 3D printer driver card. most 3 printers dont have strong support rails as such. they dont need them as there are no cutting forces involved with 3D printing. however linear support rails would be a good option for you, wanting to frame in wood. search ebay for 16mm linear support rails. then think about a motor and screw to drive to carriage. it'll be a small Nema or such like. ebay will also list 3 axis kits, interms of rails, screws and motors. take your time to look, and think about the future. you can take off the 3D printing head and bolt on a router instead and you have a fully functional small CNC in the same tool.
Phil.