Well the chutzpah of Photoshop for page layout has been well discussed.
But if you keep all the text and all the vector stuff as text and vectors on their own layers and save it as a PDF it will print out just fine with all vectors in task.
If you make it a PSD file you can edit the text later on and vectors, but it will output as raster (bitmapped/pixelated text etc.)
EPS can output both vector and raster, but once you open it again in Photoshop the file is rasterised immediately.
So in short - you can design a flyer in photoshop and have it print just fine if you save it as a PDF - but it's highly not recommended unless you're super super experienced in this dark art.
For the record I have never done this.
You're best bet is to use InDesign or Quark, or the free Scribus which isn't as good as the other two alternatives.
The thing though is that printers that you and I have at home have a native resolution output of about 150 dpi to 200 dpi (correct me if I need correcting

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Whereas a professional printers print images at 300 dpi (appox.)
As well as that professional printers and designers will design to a specific standard, for example A4 size or B5 or DL, and the item is printed on oversized paper, the excess is then trimmed away to make the exact size you need.
With home printers you won't get exactly the size you're looking for because they don't print to the edge of the paper. So BLEED wouldn't work anyway.
You'd need to design to smaller than the finished size you want, then trim it further down again.
And if you don't have a professional guilotine (I hate typing that word) then you're going to get different sizes when trimmed and possibly very poor trimming and it won't look professional.
You can do it at your own peril. But you'd be far better pleased letting the pros do what they do.
You wouldn't enter a dance competion if you couldn't dance, you wouldn't strip an engine if you weren't a mechanic, you wouldn't drive a car without a licence.
So why would you design your own flyers if you (ok I can't finish that sentence

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Best of luck with it though.