Now, before you get excited, I used to live in upstate NY, so have some experience with gardening in the northern climes.
May I suggest that you start broccoli, head and bibb lettuces inside now; onions are best started from sets, which should be available at nurseries, big box stores and on-line; leeks, I don't know, never planted them because my husband doesn't like sand in his veggies (leeks are notoriously hard to clean); spinach we direct sowed in the garden in early May.
There is probably a garden club or Master Gardeners' group in your area--contact the Agricultural Extension agent for your county and he/she can tell you about sources of help.
Welcome to gardening--it is fun, rewarding, and delicious!

Be sure to check out the Growing from Seed forum here too. Linked it below. It has lots of great FAQs on how to get started, lighting set-up, seed mixes, etc. plus lots of discussions from many that are currently starting their seeds.

Dave

Here is a link that might be useful: Growing from Seed forum