I've never been a big fan of the "mecha" series, unfortunately. In general, the complicated politics and focus on technology and combat aren't of interest to me, though there are several very well done series. But I've dabbled in it off and on over the years, both intentionally and accidentally, and there's a fair bit in the genre for everybody. The three below are more character-focused, and two are series that may fly under the radar, for mecha at least. Two of them are also among the most popular manga/anime series from the 90s.
Magic Knight Rayearth - CLAMP (3 volumes)
This was one of my favorite "surprise" mecha series of all time. While running out and buying the VHS version of the anime as it was being released, I was baffled when the light fantasy series for little girls (which the characters themselves constantly refer to as being like a video game RPG) featured the main characters hopping into mecha and combining them into a giant robot to fight the final boss. It was incongruous with the low-tech fantasy flavor of the rest of the series. Hikaru, Umi, and Fuu are three junior high girls that are pulled into the land of Cephiro for no conceivable reason while out on a trip to Tokyo Tower one day. The three girls are completely unalike, and had never met before. When they arrive in Cephiro, they receive a truncated explanation that they are chosen soldiers from another land who must save Cephiro's pillar, Emeraude. Cephiro only exists because Emeraude constantly prays for its success, but recently her prayers have been interrupted by the usual heavily armoured man in black, named Zagato. Hikaru, Umi, and Fuu receive weapons and magic powers, and must go about the business of stopping Zagato's minions as they beseech the help of the ancient Rune Gods, one for each girl, who send them on trials to determine whether they are worthy. That these spirits turn into giant robots took me by surprise, but that's one of the only surprising things about this series. Well, that and the ending, if you don't already know about it. Otherwise, it's a pretty straightforward fantasy, and at 3 volumes, not much of a commitment. I've seen the anime and read the manga too many times, but there's something enjoyable about the simplicity of this series, especially the first time through. CLAMP's artwork in the manga is quite good, and represents their earlier, more ornate period, so expect a lot of detail in the armor, the attack sequences, and lots of glitter and prettiness in general. Tokyopop printed two different editions of this, the first is numbered out of six and is a slightly oversize volume, and the other is the three-volume "100% Authentic" version. A boxset also exists. Dark Horse recently published this as a single omnibus volume as well, so it should be easy to get ahold of.
Neon Genesis Evangelion - Yoshiyuki Sadamoto / GAINAX (14 volumes)
This is the modern grandfather of most other combat/mecha series that came after. Originally an anime, Yoshiyuki Sadamoto is one of the members of GAINAX (the company behind it). This manga is one of the rare examples of an adaptation done quite well. Regrettably, I've only read about 5 volumes of the manga and seen about half of the anime series, so I can't comment too much about the deeper themes or how closely the adaptation works. But unlike most adaptations, knowledge of the original isn't integral to understanding everything that's going on, and all the necessary details from the anime are included and fleshed out nicely. Evangelion is the story of Shinji Ikari, a boy recently contacted by his estranged father. Initially excited by the reunion, his cold, calculating father quickly reveals that he only wants Shinji as a test pilot for his new robots, meant to fight off the invading "angels," foreign giants of unclear origin that are recently invading and destroying the city. The angels come in different types when they attack, so Shinji and his father's team must come up with different strategies to defeat them every time. In addition to the difficult combat, the Evangelion robots operate by "synching" with the pilot, so Shinji takes physical damage for every injury sustained by his robot. His fellow pilots are teenagers as well, and are varying degrees of emotionally remote. Much of the series focuses on the teenage pilots, the effects the combat has on them and their personal lives. Later volumes begin to reveal the larger picture, which is shockingly cosmic. Yoshiyuki Sadamoto's art is wonderful, and has a soft quality that lends itself well to the themes of the series. Viz has two older editions of this series (an older oversized edition and a modern manga-sized edition that is still being released), but their recent 3-in-1 releases are quite fantastic, and what you want to track down if you're looking to read this. It only ended last month in Japan, so it might be another year before we see the final volume in English.
Bokurano: Ours - Mohiro Kitoh (11 volumes)
This one is a slight departure, as the robot is "piloted" by a large group of teens. Only one at a time pilots it, and when that person is finished, he or she drops over dead. If they refuse to pilot the robot, the creatures destroy their town and all their loved ones with it. That's an intriguing premise, but unfortunately, the volumes I read from the first half of the series weren't that interesting. The robot is being used to protect the town from giant invaders. Apparently none of the friends and family of the teens are aware that they are making a heroic sacrifice, so there's an emotional message throughout as the characters reflect on the simple pleasures in the life they'll be giving up. One problem is that it seems to be heavily inspired by Evangelion. Piloting the robot has a very high toll on the teens since it quite literally kills them, and there's a lot of squabbling, in-fighting, and even some cliques among the group. So a lot of the emotional fallout present in Evangelion shows up here. Also, the creatures they fight are derived from Evangelion's Angels. The volumes I read followed much the same pattern, with 2-3 teens featured in each volume, each with a storyline. The star teen is the next pilot of the robot, and we learn about their life as they get their affairs in order to prepare for their inevitable demise. These storylines are usually very sentimental and sad, but the characters weren't developed well enough to draw me in. Each story segment also features the creature battle, which wound up being more interesting because the different types of creatures had different attacks, and each battle fought something like a puzzle. I hate to put it down too much, because a twist halfway through makes things more interesting, but part of me suspects the twist will only heighten the already high emotional fallout and doesn't actually change the goal or themes at all. But perhaps I'm wrong, and it has an awesome second half. As a series that runs in the Japanese magazine Ikki, it has nice-looking, serviceable art, but nothing that stood out too much. Viz is still publishing the series at the rate of about 2-3 volumes a year, and is up to 8 of 11. Previous volumes seem relatively available.