I'm a new landlord as of 2018 and did not send my handyman a W-9. I paid him well over $1,000. What should I do? Will I get in trouble?

Individual landlords are not required to issue 1099-Misc's.

Reference:  http://www.forbes.com/sites/irswatch/2013/03/06/should-landlords-be-filing-1099s-for-service-providers/

I have an LLC. Does that change things?

No, if it is a single member LLC.  A single member LLC is a "pass thru entity" for tax purposes. The schedule E is part of your personal return.

I have a partnership LLC: does this change things?

Yes. If you are filing a partnership return (form 1065), the partnership is required to issue a a 1099-Misc to any individual they more than $600.