It'll take some time to be able to pick him up, but the more you bond with him the easier it will become.
Grooming is pretty simple, with short haired rabbit you can use a comb and go down their back (not up it) until the loose fur it out, this will work well around areas with shorter fur. As for the thicker parts you can use a dog brush to detangle any fur and a comb to get it out. Just be extra careful with slicker brushes as they can hurt his skin. Remember, the less handling the better. Don't try to do it while he's in your lap or while holding him. It's best to set him on a towel in an area he's familiar with. Start by petting him then use the brush or comb so he doesn't notice. Make it quick and fun for him. Give him a little treat afterwards too.
If his nails are long you can use a small puppy nail trimmer. Its best to use a phones flashlight and set it under his nail while you trim it so you can see what you're doing. Be extra careful not to cut past the quick. If you do happen to cut past it use a paper towel and hold it there until the bleeding stops.
Here are some of my favorite grooming videos as well as one just for long haired rabbits like yours