publishing houses do exactly that....publish. They take your finished product and print it. Normally the volumes are 20,000 upwards depending on what you looking at.
What most magazine producers do is one of teo things:
(1) produce it themselves inhouse where they control the design process and ultimately th look and feel of the magazine. Also, in some cases, they think they can keep design costs down. A myth.
(2) Go by a printer broker (me) or a advertising house like CPPP or M Erickson or any up coming graphic house and let them produce it for you. The advantages of going through a printer broker is that our prices from volume printing is not matched anywhere. As a walk-in customer you wont get the same rates as an established broker that gives the print house a certain volume of work every month.
Disadvantages of going with an upcoming graphic house is experience. Most graphic artists are great in photoshop, but put them to lay out a 100 plus page document using In-design, and they're lost, which puts you, the money person at more of a strain since the pirnt houses need certain formats and specifications that junior G.Artitsts don't have a clue about. So edits and reworks come as an extra cost to you.
Guys like Narend and myself have a unique advantage of knowing BOTH print and design. So Narend can design your publication, and then work with the printers to get teh best quality (sometimes evn going on the production line to assist) out of them.
I dotn knwo what your demographic is, so i acnt make any other suggestions as yet. Sometimes, printing in other countries works to your advantage in the long run, but teh initial set up costs to form relationships with foriegn printers can take a toll.
Hit me up a PM if yu need any other advice....