I think the most important thing about playing Muscovy at the beginning is to not try and rush things. With a lot of countries, especially the smaller ones, you're in a mad rush at the beginning to seize power before your neighbors do, but for Muscovy you start out in a good position already. Your biggest fear is that you slip up and look weak, at which point your neighbors will not hesitate to swoop in for the kill.
In my first game, I pushed in aggressively on Novgorod, planning to finish them off in a few short wars, and then soon after moved in on Lithuania as well, hoping to break them as well. As it turns out, this was a huge mistake, as both wars depleted my manpower, and by the end of things I was in a spiral of doom, with everyone attacking me from all sides.
In my second game, I decided to take things more slowly. I built to my force limit, and for the most part just sat back and relaxed. Annexed vassals, built armories, had just two short wars. First one to annex Ryazan, then another to take a single province from Novgorod. Then, I sat and waited for Lithuania to show weakness. After a few more years, the opportunity came when Poland's forces were decimated in a war with Crimea, and Lithuania's manpower was also somewhat depleted. Declared war, then sat back in Moskva and let them siege. Kept close enough to pick off any stray small armies, but far enough to escape in case they tried to attack.
Eventually, between the attrition and chipping away at their armies, they were out of manpower and low on forces. At that point I struck, forcing their armies back and pushing into their land. Still, I only sieged a few provinces, got enough warscore for the two provinces I had claims on, then left taking only those and a bit of gold. This left me with almost full manpower, which I used to start another war with Novgorod, this time for more provinces since I'd been building up my claims. By this point I had annexed all of my vassals, and in this second war I was also sure to get them to release Finland, to keep from having a border with Sweden, who I allied. I had taken their colonies in the first war, but didn't pay for them and let them rot to nothing. (not worth it early game, I got them later on anyways)
At this point, I continued to whittle down Novgorod and Lithuania over time, taking things slow and only grabbing stuff I had claims on. At some point Ukraine rebelled out as a OPM, I fabricated a claim on them and force-vassalized them, then made Lithuania/Poland spit out all of it's cores over the course of a few wars, allowing me to claim a lot more land than normal and have a fairly strong vassal as well. Novgorod was eventually annexed completely, too.
During this time, I'd been getting my tech and ideas up as well, starting with Diplomacy to make claims easier and allow myself more vassals. It was only around the time that I got my second idea, which I made Religion, that I started to actually push into Horde land. I'd so far managed to avoid war with them completely, due to a combination of keeping my Agressive Expansion penalties low, my wars short and my manpower high. At this point I had gotten well ahead in tech versus the hordes, and my armies were much larger as well, so they didn't really stand any chance. Religion proved key in converting the provinces I took in short order, as were the various decisions I took that boost conversion rate, There's 4 you can take at various points, which add a total of +5% chance, which is huge. A few of them also increase revolt risk, but they are very much worth it since as long as you keep your religious uniformity high, you have very little problems with revolts anyways. Even when I got into the Time of Troubles later on, which does +10 revolt risk, I was still only at 6% RR in most provinces, which I reduced to 3% with an advisor. If I had kept my Patriarch Authority higher, I might have had none at all, though I'd lowered it mainly to fund my newly built artillery.
Once you get to this point, you're fairly safe. Just keep in mind your strengths and your weaknesses, and don't overextend. Your main adversary will likely be the Ottomans, who can easily be as strong or stronger than you at this point. The more western powers should keep to themselves, unless you overextend and get a border with Austria or something. Try to keep friendly with your western neighbors, especially Sweden and Poland, while pushing hard to the East without taking un-claimed provinces or going over 100% overextension. Past that, your wars should focus on vassalizing smaller neighbors on the baltic and possible the balkans, if you can beat the Ottomans down.
Once you reach admin tech 10, you'll want to form Russia. For me, I didn't get any claims on anything I didn't already own, but if you didn't push into europe much this is a good time to do so. Once you've pressed those claims to your content, you'll also note that you have the choice to move to St Petersburg. DON'T. (yet) Instead, work up to +3 stability, try to spend any excess MP, and start westernization. You'll need to spend a few years to get up to +0 stability, but then once you do, you can enact the St Petersburg decision, granting you another +3 stability for instant max stability with no positive stability penalties. This saves you hundreds of admin points and years of time, and as long as you don't get unlucky with events, you can easily westernize in less than 5 years. Faster, if you get +stability events and/or the Defeat Rebels mission early on.
After westernizing, you should be the premier power in the world. Keep slapping around the Hordes, use your free colonist to race for the east coast, force the HRE into a PU, whatever you want. Just don't make any foolish mistakes, such as taking too much land too quickly, or getting your armies ate by the (for now) still superior western nations. Use numbers and attrition to your advantage and nobody can beat you.