Scott a few things here. Firstly, during early season in the Sierra's there can be many hikes that are done at or just below the snowline where you can have a fun hike. By mid July you will be suprised how fast the snow is melting. If you plan on purchasing an ice ax...please learn how to use it first. On snow travel, micro spikes work well as does hiking poles. Heck even poles help a little in self arrest if you slip. You mentioned Emmigrant Wilderness, try some hikes out of Crabtree Meadows which is around 7000 feet. There are plenty of loops that can be done out of that trailhead. Also, the east side of the Sierras, especially further south on 395 has the snow melt a little earlier and offers some good hiking. Snowshoes? I use MSR's and love them! Oh and I just saw that you mentioned looking into crampons. Again, this is something that you will need to learn to use. They are not too difficulty but they need to be used correctly.
On another note, many of us in Northern California meet up for hikes each year. Join us on these please. We all have varying degrees of experience, and a lot of interesting gear that we like to show off. Each year we have a BPL California hike that is around Jan. to Feb. Keep your eyes open for it on the Trip Announcement section.
Also there are many non Sierra hikes that you can do along the coast. From The Lost Coast to Ventana Wilderness