Shall - is used with the present verb tense

    Shall we go to London on vacation next year?
    I think we shall go shopping this weekend.
    How many people shall we invite to the party?
    Shall we go now?

Tip:We usually use shall with the 1st person “I” & the 2nd person “we” only. We can use “will” instead of "shall" with the 1st, 2nd & 3rd person.

Should – can be used with the past tense, the present tense & the future verb tense
You should wake up. It is almost 0800. My sister should have called me last week. People really should start cleaning up after themselves. ] - See more at: http://english-the-easy-way.com/Confusing_English/Shall_Should.html#sthash.ypnDKP7l.dpuf