If one accepts Jesus as their Lord and Savior, does that mean they get a free ticket to heaven, or do they have to grow spiritually and form a closer relationship to the Lord? I am wondering this because of our sin and how hard Jesus says that it is for rich people to make it to heaven.
In a sense you’re right, although the ticket wasn’t free, it was just paid for by someone else. It cost the Lord His life. Growing spiritually and forming a closer relationship with Him is something the Holy Spirit helps us do after we’re saved, as an expression of the gratitude we feel for having been given our salvation. It’s not a requirement to receive it. We’re saved because of what we believe, not because of how we behave.
As for our sins, Jesus paid the full penalty for all of them at the cross, so they’re no longer an issue as far as salvation is concerned. And Jesus said it’s hard for a rich man to enter heaven because we go there due to our faith in the Lord. Many rich people have a stronger faith in their money than they do in the Lord.