It is very hard to combine quite different serifs for a text and not make something look amateurish. While it is possible, start with that thought, and if you're not sure about something, assume you're making a mistake.

As the alphabets are different, it is possible to use a somewhat different Greek and Latin font & still have harmony. But watch out for headings that don't fit.

By the way, there are more free fonts for polytonic Greek from The Greek Font Society:

http://www.greekfontsociety.gr/pages/en_typefaces1.html

Not the best, but then, neither is Gentium. For what it's worth, GFS Olga is a pretty good font, but it is offered as an an inclined only.

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In the world I live in -- scholarly books -- Goudy Old Style is reminiscent of Alumni magazines and other slick magazines aimed at people with more money than taste. While your mileage may vary, consider where you've seen Goudy Old Style used. Goudy is a Venetian, sort of, kind of. There are many better, of which Espinosa Nova is one. I mention it because just now the Roman is free, leaving you with a $50 purchase for the italic. I realize that does exceed you budget a bit.

http://www.myfonts.com/fonts/estudio-ch/espinosa-nova/

There is a GFS font (Greek) that matches it reasonably well -- if you're interested, reply so & when I get to work tomorrow, I'll look it up.

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It would appear you've got the Linotype Palatino that comes with polytonic Greek? Palatino is somewhat out of favor these days, but the OpenType version has all the characters and weights you need, and is still reasonably well respected. The fact that Palatino has been used a lot is probably the major reason it is out of favor. Designer boredom is not your problem, money is. If it were me & I had your budgetary constraints, I'd used it for all the text.

Adobe's Arno came free with some Adobe software; if you have it, it might serve your needs very well. Arno also has all the characters and weights you need. It is well outside your budget if you have to buy it, though.

& BTW, a setting size of 9-point Palatino is about the same as 10-something Arno. Point size itself isn't too meaningful these days. Fit your copy if that's a requirement, while balancing the apparent size. You probably knew that...

Good luck with it.

As to free fonts, you can try Andron and Cardo (http://www.mufi.info/fonts/). I'd prefer the new Brill font (http://www.brill.com/author-gateway/brill-fonts). Minion and Myriad come with Adobe Reader and might suit you well (after you install go to the installed folder under "resources - fonts".)

Many thanks to both of you for your help...I can tell I'm going to be using these resources for years to come. I like your suggestion of Arno, Charles...although funny you should say that about Goudy Old Style: my favorite magazine does in fact use it, which, if you're right, would put me in serious taste debt. Will play around a bit.

Again, I do appreciate your help!