I do not have a perfect idea for another Mass Effect game, but I'll tell you what I strongly feel is a terrible idea:
1. My cousin wants a game wherein you play Garrus from his days at C-Sec all the way up to the end of Mass Effect 3, including his interactions with Shepard (which would appear as your own Shepard should you import your data). I think this is a terrible idea for about a hundred reasons, including the countless retcons that would be necessary. It would probably end up being something like FF7 Dirge of Cerberus, a carnival shooter with a supporting character everyone thought was super cool right up until he had his own game and not very much to offer on his own. It's also repetition of material; we know Garm and Tarak get killed by Shepard and Garrus, so attempts to deepen them or portray their demises with new action-packed cutscenes are ineffectual.
2. MASS EFFECT: SKYLIAN BLITZ or any combination of "prequel" attempts. It's lazy, ruins the mythology, and we already know how it ends, regardless of the thin characters and side-stories and "Oh, but you didn't know about this part!" angles you insert. Nothing against Halo: Reach if you like that sort of thing, but I don't, and it will not work for this series. Need I offer an explanation as to why a "prequel trilogy" is a bad idea?
3. Anything based upon the Mass Effect novels, which, aside from being poorly written (par for the course when you hire a game-writer to write prose; no offense to anyone who enjoys the stories themselves) have nothing new to offer. They already gypped us from being able to see Gillian Grayson in a game in a sad attempt to make Kai Leng more menacing (which as you know yielded disastrous results), and now that we won't be dealing with Leng anymore, no need to flog the dead horse any further.
4. Anything that takes place during the original Mass Effect trilogy. Regardless of how cool whatever you insert may be, there's still the stigma of knowing that the Reapers will still arrive and the universe's fate will still depend on Shepard pressing one of four buttons (P.S. I like the ending apart from the treatment of the Illusive Man).
5. A Mass Effect game in which you play as a fixed character or class. Similar to the Garrus game idea, this will end up tiring and linear, and the people who have come to love BioWare for the relative openness and choice-oriented play of a game like Mass Effect will have trepidations and gripes as soon as the first teaser trailer hits.
So, what do I think -would- work? Without hashing out every detail (because as I said, I don't have a completely comprehensive idea), I'll take a shot. These are just pieces of ideas.
1. A brand new game in the same universe, with a new character (that you create from scratch, just like now) that takes place long after the end of Mass Effect 3. Problems right off the bat: how do you account for the fate-of-the-galaxy decision the player made before, and if you choose not to, how do you justify the fact that the player had any choice at all if the future civilization is exactly the same no matter what?
2. An RPG in which, Dragon Age style, the player chooses a race, gender, and class, but instead of dwarf, elf, etc, you have human, asari, krogan, and so on, all with different abilities, and the spoken dialogue can refer to her/him as something all-encompassing (e.g. "Shepard," "Warden," etc). Problems: doing different voices for every race and gender.
3. A stylized game in which the player plays as several characters from the original ME trilogy in their best moments and most interesting story arcs (this goes against why my #5 above would be a terrible idea, but hear me out for a sec). Let's say there are five stories/characters in the game, that can be played in any order (similar to Suikoden 3). Let's say, hypothetically, it's Jack, Thane, Garrus, Mordin, and Ashley - characters with starkly different abilities and personalities. You'd get to play through story arcs that happened before and during the trilogy, but all things you didn't see, e.g. Jack's time on Pragia, her stories about the couple she partnered with, the Hanar "vandalism" incident, and so on, all the way up to being imprisoned at Purgatory and released by Shepard. All of the stories would end when the character met Shepard. Present it as more stylized, a la Mass Effect 2, and ramp it up to look like a multi-volume interactive comic book (but keep the graphical style and drama and general gameplay close to what we already know from the series). Problems: How do you END something like this? What's the climax? How do you do something new with these characters apart from giving the five of them a secret mission together that Shepard never knew about? Retcons rarely work organically.
Finally, barring everything I think would WORK, what I WANT, quite simply, is another experience like the originals. Fresh, based on the same mythology, with a fairer portrayal of women (not that ME was terrible about it, but less Miranda cheesecake, more clothing, and more realistic breasts for certain characters wouldn't hurt), romance options as open and ambitious as they were in ME1 and 3, and an adventure on just as great a scale (albeit without all the Cthulu/end-of-the-universe stuff; as awesome as it was, we need something different). As for how you make it congruent with the originals after the way we left Shepard's story and the state of the galaxy apart from staging the sequel in an alternate universe, I leave that to the folks who will actually be working on the game.