The 20-year-old stopper has looked impressive in pre-season, having joined the club on the eve of their trip to Hungary.
That experience helped him to settle into life as a Spireite.
“It was a good experience and a great opportunity to bond with the lads,” he said.
“I feel part of the club now and it was a good way to break in.”
Liverpool’s youngster went out on loan to Portsmouth last season in League Two and he’s relishing the chance to play a level higher this season.
“It’s another step up and it’ll be a good test for me.
“It’s another step in the right direction and I’m looking forward to it.
“Everything is great here - the staff and the lads have been really good.
“I want to do the best I can for myself and for Chesterfield.
“I want to impress, keep improving and see what that brings.
“I could get my chance at Liverpool or I might get another loan move. I just want to keep climbing and testing myself.”
The Burnley lad thinks Chesterfield’s veterans will help the club get involved in the battle at the right end of the table.
“There are some experienced players here as well so it should hopefully be a good season for us,” he said.
“We want to start the season well and push as high as we can.
“The aim is to get promoted but it’s a tough division and there are some good teams with some very good players.
“There are players who have been around and played in the top divisions but we’ve also got that.
“We’ve got the likes of Sylvan Ebanks-Blake and Ian Evatt.
“We’ve got experienced players who have done the business.”
Fulton will start the season as the club’s number one goalkeeper while Tommy Lee recovers from a shoulder operation.
He’s expecting life to get tougher when Lee is back fully fit and raring to fight for the starting position between the posts.
He said: “Tommy Lee is injured at the moment so as soon as he recovers that will be a good test.
“There are a few lads on trial too so there could be some new faces coming in to challenge me.
“We’ll have to see who they sign up before the window closes.
“You need that competition to keep you on your toes in training and in games.”
Coming from Anfield he’s used to high expectations on the training pitch, but in his limited time working with the Chesterfield coaching staff, he’s been impressed.
“It’s a really good standard here,” he said.
“We’ve got Matt Duke and Chris Morgan as coaches who have been at really good levels. The manager Danny Wilson has also been at a top level.
“The standards are high here and so are expectations. Training in pre-season has been decent.”