Salton Sea to Cottonwood, Joshua Park

The road to Cottonwood in the park is a bit twisty and narrow, but lots of big rigs do it, and so you won't have a problem. Stop at the visitors center on the right, and register. Cottonwood is behind it about a half mile. Make sure you hike around the oasis, its pretty cool.
(The last time I was there, about a year ago, they were redoing all the roads and surely by this time the roads are finished and newly paved. All the roads are 2 lane, and 25-45MPH, lots of places to pull over and believe it or not, lots of cars on the weekends because its is a world class rock climbing area and folks come from around the world to climb around on the rocks)
Make sure you explore the park. Its about 20-30 miles from Cottonwood, maybe more, to the sites, but try not to miss Chola Gardens, Keys View, Keys Ranch (ask about tours at the Visitors Center) Hike Hidden canyon and Barker Dam, (both a little over a mile). If you need groceries 29 Palms is about the closest town, and the grocery store is on the far west end of town.(You'll think youve gone to far) Check out the Visitors Center in 29 as it also has a nice Oasis, a cute little museum is down the block and a some good restaurants in town. (If you like Mexican I recommend Enchadas, if you like hippy, Crossroads in Joshua Tree, If you like Thai, a good one in Joshua Tree also. You can make a loop by going out of the park in 29 and back in in Josha Tree. There is also a Dennys and Fast Food joints scattered around both towns. Serious shopping like WalMart etc you need to go to Yucca Valley.

OK. So far so good. Thanks.

What about the roads through Joshua Parks ? Cottonwood Springs, and Park Blvd, etc ?

No brainer, take Box Canyon, that is the ONLY way I would go. Its a pretty drive and easy doing.
Take 111 to Mecca and then turn into town and make an immediate right. Go down to the sign for Box Canyon (about 3 blocks, and take a left, following the road straight to Cottonwood. Its a pretty trip and you'll enjoy the rock formations, keep the camera handy. Hope your going soon, the JT wildflowers should be out very soon
Lots of RVs camp along Box Canyon so its well travelled

1. What's 'best'? 3.Box canyon is fine.