Lojban uses the consonants I gave (sans /j/ and /w/, although these are counted as dipthongs instead), plus /f/, /v/, /x/, /ʔ/, /h/, and /r/, as well as /ə/ for a sixth vowel. The syllable scheme seems to be largely C(C)VC(C), with largely only mixed voiced/unvoiced and geminate consonant clusters prohibited. That said, they do allow for "buffer" vowels in pronunciation to aid speakers who have trouble with consonants (and yet they have a /ə/?).
From what I can tell, CV(C) (with the second consonant usually having some restrictions) is fairly widespread. However, in my personal (purely anecdotal) experience, pronouncing foreign consonant clusters or unfamiliar final consonants is much harder than pronouncing unfamiliar initial consonants or vowels, so I'd be slightly wary of letting the final consonant go too unrestricted.
From what I can tell, CV(C) (with the second consonant usually having some restrictions) is fairly widespread. However, in my personal (purely anecdotal) experience, pronouncing foreign consonant clusters or unfamiliar final consonants is much harder than pronouncing unfamiliar initial consonants or vowels, so I'd be slightly wary of letting the final consonant go too unrestricted.