I've hiked Whitney 2x. If you're concerned about missing the permit lottery, you should still be able to get a permit in the summer. If your group is small (just you or maybe just 2 of you) and you have some flexibility in your schedule (e.g., if you already live within driving distance and don't need plane tix; you can hike during the week instead of a weekend), you should be able to secure a permit in the summer.
Keep calling the rangers office the week before you plan to hike and you'll be amazed that people do call in and cancel their permits. Also, if it's not too far away, you can be at the rangers office the day before your hike and pick up an unclaimed permit.
I got a permit in the lottery last year but then couldn't use it due to a funeral of a family member. I was surprised that I was able to get another permit in August for the 2 of us.
Whitney is a great mountain and very doable. The trail is not terribly steep, not even the 97 switchbacks... which is why the main trail is 11 miles. Acclimate for a day or two above 8000' and you'll be less likely to get a headache from the altitude. You can camp in the Whitney Portal campground right near the TH at 8300'. They don't take reservations, just walk-ins. All 3 times I've been there, I got a campsite with no problem.
Oh, BTW, if you feel adventurous and don't get a permit, you can always get up a permit for the Mountaineers Route (a class-3 climb) and go that way. The downside is that it's not too fun coming back down that way. It's nicer to go back down the main trail... but you would need a permit to do so.