As a new player how do I determine what grinds are worth going for?

In my experience;

The best grinds are those that you're either grinding multiple things at once. For example: Doing a mission that gives parts for something you want while also doing it as a Void Rift so you collect Relics (ideally also for Prime items you want). You would also, ideally, be leveling weapons simultaneously to these grinds to be grinding three things at once but as you go it gets harder and harder to have new weapons to grind.

There are a few grinds that are still very worthwhile even when they're not multi-grinds. Getting to max rank with Fortuna is one of them. Efficient grinding of Focus for the Operator (once you get it, and the Zariman) is another.

Anything passive is an instant yes. Just because.. why not?

Syndicates, for example. There's pretty much no reason to not choose a syndicate and rank them- and their ally- up.

If you're intending to do all the main quests, eventually you'll either need Entrati and Cetus standing unless you buy a Necramech either via market or player trading. You'll also want Quill standing- which you may or may not even have unlocked depending on the quests you've done- though it's not really necessary until you're pretty much endgame. It'll make life a lot easier long before that.

Doing two things or more at once is great, as Halasham says.

But most importantly, if the grind isn’t fun, don’t do it. If it’s not fun the way you’re doing it, find another way to do it. Back before they moved Harrow Systems, I spent roughly thirty hours getting it to drop in Caracol defection. It wasn’t super fun, but I made it more fun by experimenting with every frame I had to see if that frame could do the job effectively.

So to answer your question: anything that’s fun is worth doing. Because every piece of gear is worth having, and if it’s fun to get, then why not?

Do what you want. If you like the Solaris and you think the missions are fun, do Fortuna. If you don't, leave it for later when you have better gear that can do it easier. The only thing that's a must-do is progressing the star chart and the main story. There's plenty of content you can be happy never touching. Maybe one day a new update will come out and they'll add something you want, and you'll do that content then. Maybe they won't. Follow your interests.

Since you mentioned Duviri, I'm gonna assume you've done some circuit/orowyrm, so you're already getting an idea of frames/weapons you might want to have for your collection. Everyone jives with different stuff, so if it feels good to play, or sounds good on the wiki (and the grind seems reasonable), go for it. Worst case, you end up selling it after leveling it to max.

• A lot of mods are worth collecting (although some are too rare or niche to bother with). Check the wiki, look at build sites for equipment you already use, and see if anything you don't have (and can access easily) could make a big difference.
• Faction rep is always worth getting at some point (especially the ones SolOrion mentioned). When you hit MR8, you might want to grab the helminth segment from the Deimos family at rank 3, as well.

Sidenote: since the anniversary's going on right now, make sure to do any weapon alerts that come up in the next few weeks: they come with their own weapon slots (which you keep even if you delete the weapons later), and are pre-installed with catalysts.

You're already getting Rhino, which I consider to be the closest to a "must have" a new player should aim for, as far as survivability go. In regards to other frames and weapons go, if you have the time to grind one whenever a new Assassination unlocks, go for it. Don't need to be all at once, sometimes the RNG is cruel, but make a note of any that you skip. You'll probably want to avoid the really annoying grinds, like Trinity, Equinox or Protea; thankfully they all have Prime versions now, but even that will be a matter of time.

You may also do some Nightmare missions, or crack Relics (if you're earning them, of course), weekly Ayatan or Clem, etc.

For Syndicates, try to not overdo yourself, they can feel a little too much. From the basic ones, pick one of the sides (there's three on the left and three on the right) which will all synergize with each other, and just do basic missions while having a Pledge. For all the bounty-related groups, pick one or two and do a few missions when you're able. If that's too much for a single day, just pick one and go at your own pace.

As you climb through MR, check the Market for new blueprints unlocks. At MR6 you should have access to the Kohm, the Hek and the Atomos, which are all fairly great new player weapons. If you're in a clan, check out for the Ignis Wraith as well.

And when you find a couple of weapons that feel comfortable, try to level up the ones that aren't so good to earn a little MR along the way. Put either your favorite primary or secondary, and then equip level 0 weapons on the other spaces and get some affinity. You don't need to always do this, but its important to not let the MR linger too long.

In general, Warframe is a game that's best enjoyed at your own pace. There are very few timed events, and even fewer that are rare (Plague Star and the seasonal ones come to mind), so you rarely feel like you're missing out on something.