In his blog post Some Thoughts on Open and Closed Communion, John Bellingham makes three interesting points about the relationship of baptism and the Lord's supper.
"1) Water Baptism precedes the Lord's Supper in the apostolic pattern...the order of events in Acts 2 does seem to lend considerable support to the practice of closed communion, viz. Repentance (v. 38) --> Water Baptism (v. 38) --> Church Membership (v. 41) -->Lord's Supper (v. 42)."
"2) Water Baptism precedes the Lord's Supper in the order of their institution...Jesus instituted Water Baptism at the beginning of His earthly ministry and the Lord's Supper on the same night that He was betrayed."
"3) Water Baptism precedes the Lord's Supper in their doctrinal order...just as a baby must be born before she can eat and be nourished, so the ordinance symbolizing new spiritual life doctrinally precedes the ordinance symbolizing ongoing nourishment and sustenance. To reverse this order is to confuse the doctrinal significance of these two ordinances."
Read the entire piece at the link above.