cell phone carriers sell there phones in a locked mode not allowing them to be used with any carrier other then themselves (mostly for subsidizing reasons) however all GSM cell phones can be purchased in an unlocked state also which allows them to be used by any GSM provider.
Many phone can also be unlocked, some for free some for a small price some not at all (newest nokia smartphones)
now since you are on cingular when looking for a phone they main thing to need to look for is that it can be used on the 850 band
most phones are triband either 900/1800/1900 or 850/1800/1900 you need the second one or one that is quad band 850/900/1800/1900 (you just need the 850 part)
now for phones it depends how well you want to browse in full html
yes yuo can download the java based opera mini and use it on almost all phones and it is pretty nice. however i like the options and viewing ability of the 3 main s60 browsers Opera 8.5 Netfront 3.3 and ThunderHawk (do a google search for any of them)
now most phones nowadays have a built in mp3 player and from what i have read sony ericson is on top of the others but i personally have a nokia 6682 and with the built in app i think it sounds great (just get yourself the ad-15 adapter and a nice set of headphones)
WiFi is mainly for browsing the internet faster for streaming music and video much faster then you can over edge
Since you have said mony isnt really an object time is the only real concern probably the best phone (non pda type) that i can suggest would be the n80 a nokia slider s60 smartphone (google "n80 nokia") as most people will agree that phone is sexy in many ways

only thing is that it isnt actually out yet