I know what it is like to make these decisions. You do not say what if any options you may have other than a separate storage facility. Family would be best.
What ever you do, you need someone here that has power of attorney so they may act if the storage place closes, is sold to new owners, etc. where a document needs to be signed.
You need to prep the car correctly and drain and purge all the gas.
Make sure family and friends have written statements of your intentions for the car and not to sell it from under you.
Make sure the title is available, rather than in a safe deposit box in a bank that no one can get into.
If your only option is outside storage, consider selling it before you go.
My experience is that inside climate controlled storage facilities will not do cars, a regular large unit may run you $100 a month depending on where it is. You need to check around. Is the car worth that much cash to you?
1968, hardtop, 289, C4, seafoam green.
1966, hardtop, 289, original 3 speed, on the road and fun to drive.
1968, hardtop, 200, 3 speed, in work.