"no matter what type of phone you get here, it will NOT work well in Europe";
This is absolute B.S.
I, as well as friends and family members, have taken many phones to Europe that were purchased in the US (dumbphones and smartphones), and they worked fine. The key, as you already know, is that the phone must have the correct frequencies (bands) and type of technology. North American phones can use GSM or CDMA or both, while European phones only use GSM. And for 2G service, North America uses the 850 and 1900 frequencies, while Europe uses 900 and 1800. Therefore, you need a quad band GSM phone, which will work in all countries that use the GSM system.
It is true that older and/or cheaper phones may not have all four bands. Many basic "dumbphones" had only the two bands for the continent where they were sold. So, if you have one of these bought in the US, it will not work in Europe. But a quad band phone certainly will. And if it's unlocked, you can put in any SIM card you want.
A triband phone will have two frequencies for one continent, and only one for the other; it may or may not work well, depending on which frequency the local carrier and local towers are using. Maybe that is what the salesman was referring to (to give him the benefit of the doubt). But these are now hard to find; newer phones are almost all quadband, except for cheaper dual band phones as I said above.
Of course, you do have to double-check any phone's specs before you buy it. But it needn't be a new or fancy phone; all Motorola RAZR's made for T-Mobile and AT&T were quadband, for example.