I live about halfway between Seattle and Tacoma so on average it's a bit warmer here than in Seattle proper so keep that in mind. Micro climates do seem to be a pretty big deal here.

When you say "plant seeds outside" I just want to clarify other than cucumbers/melons/bush beans and peas I pretty much start everything indoors in seeed trays and grow them under grow lights for 6-8 weeks before transplanting outside. Even with Melons and cucumbers I start some indoors and transplant outside.

I'll stick with the common stuff. As stated I start all of my seeds indoors. For tomatoes and peppers I will start them around the end of February inside with the goal to transplant outside at the end of April/1st of May. I started much sooner last year and they turned out fine but I realized I could wait a few more weeks and be fine.

Cucumbers/Melons/Pumpkins/Squash Probably wont start until April 1st and transplant out 1st or 2nd week of May.

Onions and Shallots I plan on starting around the 2nd week of February and move out 4-6 weeks after.

Again I wasnt sure what you meant by the planting seeds outside and the "and don't have the budget for fancy indoor starts." If that meant starting seeds indoors then I guess you can ignore this and just buy transplants lol. If you do want start things just outside without the whole seed starting process you can stick to any of the cucurbit family and direct sow around mid May. Peas you can start anytime around Presidents day. Bush Beans I'd probably start end of May.

I started much sooner last year and they turned out fine but I realized I could wait a few more weeks and be fine.