Prepare to be confused.  The office machine market has changed radically since i got out of the business 15 years ago. however a few things are still basic.

The first thing you need to do is decide what your use is.  A couple copies every few days is a lot different than 3,000 or 10,000 a month.  Also you need to decide what features you need. Do you need legal or 11 x 17 paper?  Document feeder?  reduction and enlargement?

For sake of discussion I will assume you are a low volume use kind of like me. I copy anything I send to landowners and put it in a folder. I don't have a copier any more.  I do have a Samsung desktop laser printer

that works as a copier.  It has very limited reduction/enlargement and only does letter size paper.  It also only cost about $150. 

Where things get confusing is the type of printer involved.  Historically a xerographic printer (plain old copier or laser printer) has been cheaper to operate than an inkjet printer. Mom has a Canon inkjet printer

she uses as a copier.  It is not connected to a computer. Works great, copies in color, copies photos pretty good, doesn't take much space ... but her cost per copy is a lot higher than her old black and white Sharp copier it replaced. (edit) BTW, this has separate color tanks.  If red runs out all you replace is red, not a cartridge with everything else in it.  That is one feature I would insist on in an inkjet printer for anything beyond very occasional use.

My laser only prints in black and white, doesn't copy photos very well, and cost a lot less per copy than hers does.  And since I found a toner refill supplier it costs even less.

Most copiers either will or can work as a printer.  That is great! Once you get used to it you'll love it.  My Samsung is old enough it has a USB and a Centronics port.  I have 2 computers connected to one printer, which is also my cheapest to use printer.  Our church has the office computer tied to the copier.  Now printing bulletins means touch that computer button and every copy is an original.

(edit) Just realized I misread your desire for a fax. If you read this as I posted it originally  you'll see a changed paragraph.  Most of the "multi-function" printers will have a fax because it costs so little for the manufacturer to add it.  The new digital copiers are basically a fax machine in a copier box.

Among the big decisions is ink jet versus laser.  Ink jet will probably cost less to buy, makes lots prettier copies, and costs a lot more to use.  It's back to making decisions about your use again.

And if you walk in to the office supply store and say "I just want a copier"  They will look at you really dumb, because they don't have a clue what you are talking about