When there are 4 beats in a bar and you have 8 quavers, the rhythms that you're talking about, despite being in groups of 3, aren't really triplets. Triplets are usually 3 quavers squeezed evenly into a space that would usually only house 2. If they were triplets, you would only have 3 beats in the bar and would be in 3/4 time - a different rhythm and feel to what I think you're describing.
In your song you've got a syncopated rhythm, 8 quavers with emphasis on the beats in bold:
1 (+2) + (3+) 4 (+)
When music is written down, the purpose of the time signature is to make it clear to the musician reading the piece (who may never have heard it) where the accents fall and how the groove is generally grouped.
With that in mind, you could write it in 4/4 time and most people would say that it would be correct, but I agree with the previous poster who said 3+3+2/8
It makes it much clearer what the feel of the song is - but then you could write it in 4/4 and make it clear in the way you group the notes; as long as it's clear where the emphasis is it doesn't really matter.
Things like that matter less when you're playing together and everyone knows the feel, and more when you're trying to record or play to a metronome. For example, when you're playing to a click track and the clicks are just going 1, 2, 3, 4 - that 4/4 feel is quite off-putting. I just had this experience recording a guitar arrangement of Stand By Me where the bassline is syncopated. I ended up recording a loop of the 123 123 12 rhythm to use as a click track to keep the feel.