I guess I'll have to give it a more thorough look. My first impressions could have been wrong.
Also I see the Tekken movie on there too. That was the second anime my brother owned but I was allowed to see that one.
I'm kinda guessing that whatever other anime he did have had a bucket-load of fan-service and/or nudity in it that he didn't want you to see.
And that would mean that it could have been an
OVA series, and not a TV series, since OVAs from the 1990s were notable for getting away with a lot more violence and nudity than TV series, and there were a lot of those types of OVAs made back then. Gunsmith Cats was also an OVA series, so that would fit as well. Notably, Nadesico was a TV series, so this theory would rule it out. We can narrow it down then almost certainly to some late 1990s or early 2000s OVA series that has mecha + boobs.
Edit: I started looking at OVAs from the first quarter of 1995, and immediately came across
Armitage III. 1995 OVA, set on Mars, labeled as mecha, with a lot of fanservice, episodes were also being released in a time-period overlapping Gunsmith Cats, so it's not unlikely they all got picked up around the same time, and the trailer reveals a similar genre. Also a pretty well-known title so there could have been copies floating around. However, looking back you did say that it was Mars with bunkers + mecha battles, so this one doesn't seem to quite fit that bill.
https://www.youtube.com/watch?v=gAj7o9IJBxQ