FLAC converting to M4A

I use Foobar 2000 to convert from FLAC to 320kbps mp3 and then import these directly into iTunes. FLAC -> ALAC has no quality loss (its just a different wrapper around uncompressed 16/44.1 audio data). Converting FLAC to a lossy format and then converting this to AAC would give an unneeded quality loss.

Yes, FLAC to ALAC is lossless, it doesn't change the audio at all - i.e., you could convert WAV (CD audio) to FLAC, to ALAC, and back to WAV and the 2nd WAV file should be bit-for-bit identical to the first one.

AAC is lossy - it is very similar to mp3 but uses a slightly different (claimed to be better) compression algorithm. Its actually been developed as the successor to mp3. At higher bit rates (256kbps or higher) the difference between mp3 and AAC is marginal, and audible differences are more likely to result from the encoding s/w rather than the algorithm itself. If you want to use lower bit rates (less than 128kbps) then AAC may give better results (i.e., less perceived quality loss) than mp3.

If you want to convert from FLAC to AAC best bet is to do so outside iTunes - again Foobar2000 is one (of many) apps that will allow you to do this. Foobar's AAC converter supports multiple modes depending in usage; with VBR (the best option for use with iTunes) you can select bit rates from approx 20 kbps up to 400 kpbs. 256kbps would be consistent with the "high quality" option for CD import in iTunes.

One additional comment ...

.m4a is the standard file extension for any media encoded using MPEG-4. It provides a common "container" for a variety of formats. Its slightly confusing, I know, but the m4a container is used for both AAC (lossy) and ALAC (lossless) audio. Referring to audio data as "m4a" doesn't therefore imply a specific compression method. Your original question talks about using 3rd party software to convert to "ALAC or M4A" and then converting to AAC. In this case "M4A" and "AAC" are synonymous - and you definitely want to avoid anything that converts FLAC to lossy M4A and then converting this again - every conversion to a lossy format involves quality loss.

If you want a reasonable compromise between file size and quality, use your software to convert FLAC to either mp3 or m4a (i.e., AAC) at 256kpbs. I'm not familiar with Bigasoft but I assume that it'll allow you to add/update any metadata (artist, album name, track name, disc number, track number, etc.) either before or after conversion from FLAC. Then import the resulting files into iTunes. Don't attempt any further conversion within iTunes. Using mp3 may have (slight) advantages if you want to play music using other software and/or copy it to non-Apple devices (though these increasingly support m4a/AAC as well.

That sounds fine. I always aim to have the output from converting FLAC go to a pre-determined folder and then use File > Add Folder to Library ,,,

Adding the metadata in iTunes isn't a problem - the only reason I do it in Foobar is because most if the FLAC encoded content I add to iTunes is recordings from the Live Music Archive or similar sources of concert recordings, many of which have no metadata at all in the FLAC files or, even worse, have minimal and inconsistent metadata, If you convert these to m4a/mp3 without adding basic metadata you risk getting the dreaded "Unknown Album" by "Unknown Artist" in iTunes, or tracks that should be collected together distributed across a number of albums in iTunes. However, there is no functional difference between adding the metadata in iTunes or in another tool.

You may try Audacity which is free to convert FLAC to M4A

You may also tryiDealshare VideoGo which can batch convert FLAC to Apple Lossless, M4A, WAV, AIFF, DTS, AAC, WMA, AAC, etc as well as convert FLAC to M4A.