Lets just start with the equity accounts. The current set-up with the 5 accounts appears to be correct.
1) Common stock never changes unless you issue and purchase additional stock
2) Retained earnings are prior years accumulated earnings and losses
3) Shareholder capital is the account that everything will roll into
4) Shareholder contributions is money contributed in the current year
5) Shareholder distributions is money taken out of the business in the current year
On January 1 before you make any transactions you look at the balances of accounts 2, 4 and 5. You zero these out into account 3. You start the year with only common stock and shareholder capital.