I'd never say 'go shop'. In British English, activities beginning with 'go' always use a gerund - for example, go swimming, go sailing, go shopping. Following 'go' with a bare infinitive would be ungrammatical. Connotations of 'go shop'? It sounds like Informal spoken American English.

Shop is an imperative. Shopping is a process that take place when you speak.

'Go shopping' is the verb + activity, like go swimming, go jogging. 'Go shop' sounds a little rude and means that you should go shopping, it is an order! Hope this helps Bob