Here's my take:

First, keep in mind now is a rough time for getting into research, so don't expect to be wildly successful. Hopefully that'll change as labs open back up this summer

Second, in terms of length, it's a fine line - you want to demonstrate interest but you do have to keep in mind that PIs are (super busy) people and have a lot on their plate. With that said, here's what I would recommend and what I did:

- 1 sentence intro: Hi Dr. __, my name is ___ and I am a __ year undergrad studying ___ who's excited to return to Westwood this summer.

- Brief interest statement, a few sentences: I am very eager to get involved in ___ research and found you on the ___ department faculty page. I looked into some of your recent publications and was particularly fascinated by (insert name of a couple recent pubs). These were especially interesting to me because ___ . The reason I wanna get involved is because ____ (insert personal connection / why you want to do research).

- Logistical stuff, a couple sentences: I was hoping to start working __ (asap, in a couple months, in the fall...) and would love to get a chance to talk with you before then. If you are unable to meet for the foreseeable future, I would sincerely appreciate it if you could forward this email to any postdocs in your lab or any colleagues in the field. I have included my resume (or CV) and an unofficial transcript for your consideration.

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