Equity is how much value the company owes you the owner. It is calculated by this formula, total assets less total liabilities.
Do not use vendor accounts for equity transactions.
You can post both investment and drawings to the equity account, nothing wrong with that, but it does make it hard to see at a glance what that activity looks like. As a result, I suggest for sole proprietors and partnerships the owner/partner equity accounts look like this:
[name] Equity (do not post to this account it is a summing account)
>> Equity ( first of the year roll up drawing and investment into this account as well as retained earnings)
>> Equity Drawing (record the value you take from the business here)
>> Equity Investment (record the value you put into the business here)
During the year you can run a balance sheet to see the totals in the investment and drawing accounts easily.