If you don't score in the lottery, note the April 1 and May 1 situations in the Inyo N.F. Permit Reservations
Guided tours: I think they are all via the Mountaineers Route, and expensive. I've not seen them doing summer trips -- only early spring, via the Mountaineers Route.
Cottonwood Pass to Whitney summit is a 3-day backpack for most people. And unless you can score the Trail Crest Exit permit to go down the Main Trail, you have to exit the same route, so 5 days total, unless you're faster than average. That route is all on trail, non-technical. (A mountaineers route exit is feasible, but not advisable, or even safe, for first-timers.)
Be sure to enter the lottery. If your gf also enters, make sure you don't name each other as co-leaders, or use the same address, as that would cause rejection due to multiple entries.
In a heavy snow year, June can add technical issues (crampons & ice axe) to the Main Trail route. This year started out super-draught, but has caught up some so far. You'll have to wait and see regarding June for snow levels.
I don't think C-19 has changed anything as for quotas. It did change the permit pickup process last year--no in-person pick ups, and no last-minute permits available. In the past, last-minute permits were available due to no-shows and cancellations, the day before entry. I am hopeful that will return this year, and it is the last resort to getting permits.
If you do score a permit, read up on altitude acclimatization and AMS (Acute Mountain Sickness). It wouldn't be fun proposing while puking -- or having to turn around due to AMS.