Common in Germanic languages is a series of 'lax' vs. a series of 'tense' vowels. These are commonly refered to as having a long vs short distinction, but in many languages it is as much a difference in quality as a difference in length. In that perspective, the distinction between /ʏ/ and /y:/, which exists in several Germanic languages, is both a distinction in length and quality. So /ʏ/ and /y/ are distinct, but this distinction also comes with a difference in length.
Since all Germanic languages, save Icelandic, have a length distinction, often accompanied by a slight difference in quality, we ought to make a similar distinction. A possible vowel inventory we could have, would be like this:
Long/Tense:
/i:/
/y:/
/u:/
/e:/
/ø:/
/o:/
/a:/*
Short/Lax:
/ɪ/
/ʏ/
/u/**
/ɛ/
/œ/
/ɔ/
/a/*
*/a: a/ could also be /a: ɑ/ or even /ɑ: ɑ/.
**/u/ could be /ʊ/. That would follow the principle of the tense/lax distinction, but not all languages use /ʊ/, some rather just have a short /u/.
These series would like be accompanied by a schwa, which seems to be present in most if not all Germanic languages.
This set is based mostly on German and Norwegian, which seem to have the most systematic vowel inventories.
Some Germanic languages might not corrospond neatly with this set, but those generally have an unbalanced and unsystematic vowel inventory. I believe it is easier for an auxlang to have an inventory without any weird gaps or presence of vowels that are uncommon in Germanic languages. An inventory similar to what I proposed above is easy to pronounce for most speakers of Germanic languages and is relatively easy to learn becuase it's nice and systematic and all
.
A possible consideration is if we want the difference in quality between long and short, since not all Germanic languages have it. We could have the distinction in length be obliged and the difference in quality be allophonic, in free variation.