I would personally start with the logo, get that right first. Then i'd apply that logo and style to letterheads, comps slips and business cards. Website will come afterwards.
Create your logo as a vector using in Illustrator - you can also do this in InDesign.
I would personally do the vector logo in Illustrator and copy the vector over to InDesign and use InDesign to layout the artwork (simply Apple+C in Illustrator, then open up a new document in InDesign and Apple+V - or control+v for PC).
I would deliver the artwork as a PDF, make sure you convert all text to outlines to avoid problems with fonts. Find out from the printers if they require bleed on the artwork (most do) and if they have a particular PDF setting they use get them to send it you so you can save your PDFs to these.
When delivering the artwork for print talk to your printers get them to give you as much info as you need. Get a good relationship with them, the more work you put their way the more favours you get in return.