You go for the BPA. Drafting by position is only considered if you don't see yourself getting good value from the BPA (i.e. difference between 10 OA and 20 OA not that much). Even then, trading down is probably preferrable to going after a guy ranked lower, and just hope you get him when you move down.
The Leafs currently need 1C, Power Forwards and 1G.
1Cs usually take 4-5 years to develop, power-forwards take 3-4 years and goalies usually take 5-6 years.
Drafting for any of those positions now doesn't help us immediately. Getting the BPA and having a solid, tangible asset to offer in a trade to get help now is the best option to fix current issues.