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For faxing, we bought a little modem for around £10 (I think). Was less risky than buying a more expensive all-in-one with worse reviews and more expensive ink!
I have a Canon MP600R and it's pretty decent quality. It's a couple of years old now, but I believe there was a version with fax on it. I'm sure there must be similar newer versions that they make now.
For cheaper/ink AIO printers I tend to recommend HP.
In particular the HP 6500. Cheap but robust enough.
But do agree with getting a cheap B&W lazer fax.
I used to have a b&w laser and a colour inkjet and a scanner with a fax modem, I now have a colour laser (with duplex) with the scanner. Works out cheaper per page using a laser and without the mess of inkjet (I tried refills, refill kits and bulk ink tank and all were messy)
I used to have an all in one, which appeared to do it all - but always failed and the drivers were frnakly crap. Now I use separates and have a wonderful xerox duplex color laser printer, a flat bed scanner and no bloody hassles.