The Ultimates volume 1 & 2 uniforms do look a bit Matrixy, but to be fair the first scene that introduced us to Natasha and Clint was pretty much the lobby scene from matrix.
I would rather not have that uniform. But I do want him in costume. I think some semblance of his Ultimates Vol 3 uniform combined with elements of his current (Hawkeye and Mockingbird - NOT Bendis Avengers) 616 costume would work well. Those who think purple, or spandex(ish), or a mask, or the loincloth thingie would look ridiculous and ill-fitting for a military man/SHIELD agent are entitled to their opinions, and have a point, to a degree. But if we use this spin on Clint, then those parts of his uniform not only will look fine, but will also fit with his status as a SHIELD special agent, and with his personality and the nature of change to create a superhero team - not a superpowered special forces team.
Backstory starts off as in 616 - Clint Barton raised with his brother in the circus, and mentored in archery, sword fighting, and acrobatics by the Swordsman and Trickshot. Switch it up a little, and years later, after finding out his mentors are in fact criminals using the circus as a means of moving from town to town and them having brought his brother on board, Clint joins the Marines and becomes a sniper. He serves several tours before finding killing is getting to him and decides to retire. SHIELD however doesn't want to lose such a phenomenal skill, so offers him a position with them, where he takes up the bow again as a means of using his skill, but with more room for incapacitating, wounding and disarming without killing (except when absolutely necessary of course). He becomes comfortable in this role, and the performer side of him starts to come out again, acrobatics and bravado becoming more and more a part of his approach. Perfect candidate for the Avenger Initiative.
Brighter colours, tighter fitting clothes, and even the loin cloth and mask would therefore suit his performer/soldier/acrobat/archer/ more.