I would strongly recommend against a latex paint for this application. It will scuff too easily and not last, and you will regret it.
Use the oil. I can highly recommend Sherwin Williams Industrial Enamel as a top coat. It is VERY durable and washable too.
Wait until the weather is good so you can keep the windows open.
For the vinyl floors, the best you can do is use Oil Based Floor Enamel. Make sure the floors do not contain asbestos then clean and scuff sand the floors before applying the paint. Walk carefully in socks on the floor for the first 2 weeks after drying as it takes time to cure and fully harden.
New vinyl flooring would both look better and last longer.