As already mentioned these days music tracks purchased from the iTunes Store are all 256kbps AAC format.
I perfectly understand the need to use something like AAC for your iPhone due to the more limited storage of an iPhone compared to a computer. Apple also realise this - or do so now. 😉
Oldtimers will recall that Apple sold a version of iPod called the 'iPod Shuffle' this was little more than a USB memory stick with a headphone port. Like USB memory sticks it had a very limited amount of storage, as a result Apple chose to automatically convert any high quality music tracks to AAC format when being synced to an iPod Shuffle, this allowed you to keep your computer iTunes library with full CD quality tracks e.g. in Apple Lossless format but automatically sync them in a lower quality but much smaller file size when syncing to an iPod Shuffle without needing to make duplicate copies.
Time moved on and Apple introduced the iPod Touch and the iPhone both of which like the iPod Shuffle use flash memory for storage and have less capacity than a computer and also less capacity than the 'iPod Classic'. However at this time Apple did not provide the ability for iTunes to auto convert when syncing like they did for the iPod Shuffle. I actually contacted Apple about this and asked them to add the ability to do this for syncing to iPhones etc. for the same reason and I must have been successfully because they did subsequently add this ability when syncing to iPhones etc.
You can therefore do the following and still have your computers iTunes library with potentially just Apple Lossless tracks and use AAC on your iPhone. See http://www.ilounge.com/index.php/articles/comments/syncing-lossless-tracks-to-ip od-as-aac-files
As an aside here is my perspective on choice of music format.
Apple Lossles aka ALAC, FLAC, AIFF and WAV are all lossless formats and if the track is from an original audio CD all of these formats will keep the same exact quality as the original audio CD. AIFF and WAV will require exactly the same amount of storage space as the track does on the CD, whereas ALAC and FLAC being compressed but still lossless will take less space. Roughly speaking ALAC and FLAC use the same amount of space and compared to the AIFF, WAV or CD track this will be about half the space.
Let me repeat ALAC, FLAC, AIFF and WAV should all sound the same since they are all lossless copies of the audio CD track.
So in terms of audio quality vs file size ALAC and FLAC are roughly equal and both are superior to AIFF and WAV.
The next issues to consider are usability and compatibility.
Some programs can support things like embedding album artwork and meta tags in AIFF files e.g. iTunes, some programs can do this for WAV files e.g. Windows Media Player. However iTunes cannot do this for WAV files and WMP cannot do this for AIFF files. Both iTunes and WMP can however do this for ALAC files.
Note: iTunes does not support FLAC files so obviously it cannot do this for FLAC files.
Therefore ALAC is the better choice if you want to use the same lossless quality track in both iTunes and WMP.
It is possible to fully use ALAC files in WMP and even Microsoft Media Center in Windows XP onwards although for XP, Vista, and 7 you need to install both an additional codec and a meta tag handler. For Windows 8 and 8.1 WMP has a built-in ALAC codec but still needs a meta tag handler, for Windows 10 WMP has full built-in support for ALAC even down to embedded album artwork meaning nothing extra needs to be installed. As it happens I came up with the original solution to allow WMP in Windows XP to play ALAC files and was therefore the very first person to do this in the entire world.
ALAC these days is a free open-source format - hence it now being officially supported by Microsoft, and it is also supported by many other programs and devices, e.g. Foobar2000, WinAmp, dbPowerAmp, WMP, Media Center, VLC, Plex, KodiTV, Sonos, Logitech Squeezebox, etc. etc. and of course all Apple's devices such as iPod, iPhones, iPads and Apple TV.
Therefore unless you are using a device e.g. Android which does not support Apple Lossless you should I suggest use Apple Lossless rather than FLAC, AIFF or WAV.