Gmail is free. It used to be frowned upon for business, but like so many aspects of working online, that has changed. I now use Gmail almost exclusively since the email associated with my website gets TONS of spam and Gmail has a very good spam filter. Alternatively, will your internet provider let you set up an email for your business? Most allow multiple email addresses per account. (I'm in Canada, so things might not be the same where you are.)
As for website builders, many small businesses that don't have a lot of content but want a basic presence use SquareSpace or Wix. Wordpress also offers free websites with templates, but you have to do a bit of work to make them look good. No matter which platform you choose, be sure to do your SEO so people can find you.
I'm with Julie about using Instagram over Facebook for social media. I'm not sure if this is still the case, but FB used to throttle traffic to encourage businesses to pay for exposure (the old "pay to promote"). Of course, if your followers are on a particular platform, go with that.