The best way to describe TMNTA is that it aged with the audience. It started out as cartoon episode adaptations and when it began new material it was good stuff but nothing shocking or controversial and there are a few early arcs that I cannot stand.
But the series gets very cerebral and even dark toward the end and it has the most solid ongoing narrative of any TMNT comic; it flows very well.
It isn't blood and nudity and cursing; not that kind of "mature". But the stories are very smartly written, the characterization is strong and the arcs are suitably epic. It's a very well-rounded series suitable for all ages, but that doesn't mean it is insipidly kiddy, either.
I dunno if I can recommend the "Future Tense" trade. It was a very poorly put together book, collecting random issues around a "theme", but the arcs lose their strength without any of the build up or context from the preceding issues. Its also in black and white, but more importantly, it's missing a page of content. Again, a very poorly put together trade. The missing page was posted on TMNT.com for a while, but when Viacom took the site over they removed it. So yeah.
It's vertainly better than nothing, and it collects some of the later issues that can be hard/expensive to track down. So if there's no other alternative, then go for it. But I honestly think TMNTA is a series best read from beginning to end to get the full impact.
The Technodrome's own Demon Alucard made
This very hand guide to the Fleetway series, detailing which issues contained reprints and which contained original material.
So if you can recall the covers, that should tell you what you got.