Let's say my full position is 400 shares. I might buy 100 shares to start my position. Watch for company news, watch how the stock trades versus the market. Then if all looks good, buy a second 100 shares; half a position. Repeat until I get to a full position. Sometimes I dawdle too much and do not get to my full position because the stock goes up and gets away from me. I'm OK with the stock goes up part of it and will wait for a pullback.
If during the process of buying for my taxable account, I really see very little downside risk, or see a great price, I may buy for a tax deferred or tax exempt account.