She's worn two different combat spec ops suits while she was with the Facility. She had a black and yellow combat spec ops training suit. This suit was never shown if it was used in the field. She then had a solid black combat spec ops suit with a wristband timer that was shown to be used on missions, including her final one of escaping and destroying the Facility location she was kept in with her mother.
While confronting Wolverine in the finale, Laura switches it up to a more updated with her age combat attire. This same outfit wouldn't be used again after this fight. A variation of the cover version though is used during her Academy X days, and then that version also made its way into the Marvel vs Capcom 3 video game as her default costume.
During her first run with the X-Men right after NYX, she donned a female version of Wolverine's Fang suit that was from a Night Club that focused on the waitresses dressing up as various superheroes. Much of the hostess attire at the club was gender bent or revealing so as to better cater to their patrons and to help boost patronage with word of mouth.
Captain Universe/X-23 One Shot
During a brief one shot comic appearance that featured as part of a multi-oneshot storyline around the Captain Universe entity, we're shown an only once used new tan and blue costume. We end up also seeing a slight variation on it as we get to see said costume with a fraction of the Captain Universe power bestowed.
Academy X: New X-Men
At first with the New X-Men, Laura returned to her more familiar sleeveless black combat Facility covert-ops attire. Then later switched to the suit seen on the Target X miniseries 6th issue cover as is also seen in Marvel vs Capcom 3. Then it started taking a more purple hue. Soon it was followed by a form of graduation suit in an iconic yellow and black as the students formally became the New X-Men.
During X-Force she donned another spec ops suit. This one in silver and black with a black and red belt emblem. This masked suit was to help them keep a low profile for more covert stealth missions not tied formally to the X-Men.
Much later after much switching between her Yellow/black iconic suit and her silver/black spec ops masked suit, she finally settled on another new iteration. Retiring her student yellow/black costume, she switched permanently to her X-Force suit, this time without the mask, and opted to carry the X-Men "X" logo in yellow and red.
During the oneshot and then the ongoing comic run, she stuck with her newly revised suit, but mostly opted to stay in civilian clothes. We were treated though to seeing her in a full on Captain Universe garb at one point in the short lived ongoing comic. Showing us how she would look entirely donned in its full power.
At first with the Avengers Academy, she stuck with her most recent X-Men suit, but later during her tenure, X-23 switched to a more blue and black look that had an alternating series of tops. The tops varied from a bikini top, to a more supportive one, and then eventually a full costume.
Starting in Avengers Arena, Laura has switched to a much more wrapped type costume. The reason for this change was never elaborated on nor explained. It may have been to reflect the recent events in Avengers Academy where she felt used and manipulated again. A bandaged costume to reflect how she may have become more withdrawn into herself from the experience. Something to tie herself back and remind her of her inner turmoil of what Finesse did.
All New X-Men
With joining the All New X-Men, X-23 will be receiving a new costume that fits in with theirs. We've already seen two variations of this suit. One is a more cleavage revealing suit that doesn't seem to fit with the costume styles, and in the following issue's cover we're shown that it's a much more covered suit without showing skin directly over her vital spots.