cover crop from now until July 1 in PA

Hello!

Total newbie here! I've never grown anything outside of kitchen herbs.

We just bought a property in Central PA and we will be taking possession at the end of June. The sellers are offering to let me come in and do some plantings in the garden prior to closing. I was thinking of just planting some cover crops in the raised beds (about 500 sqft) and then planting some short season and/or fall crops. Any suggestions of what cover crop to plant?

Will they let you come in and care for it or is this a one shot deal until July?

Buckwheat is the standard for fast biomass, you could get a couple crops through the system by then.
Peas would be my choice for nitrogen fixing in a garden. Clover is too hard to kill sometimes.
Oats, rye, wheat will all make a cover crop cheap and easy--just buy a bag from the feedstore and spread it by hand. I would put out the whole bag of oats and rake them in.

I think I can have access to the land more than once but I don't want to make it a regular thing. I was thinking of planting the cover crops during the inspection and then turning them under when we get the keys on June 23rd. That's about 10 weeks. I think I'll skip the buckwheat and go for peas, oats, and vetch.