Walcott produced a stunning individual display with a hat-trick as Premier League newboys Blackpool were ripped apart 6-0 at Emirates Stadium on Saturday.
The 21-year-old was a controversial omission from Fabio Capello's ill-fated World Cup squad, only to be welcomed back into the England fold following the dismal display in South Africa.
Despite now winning the plaudits the former Southampton trainee knows there is plenty of hard work still ahead.
"I had a nice break, mentally, through the summer so I could think about things and am pushing on now," said Walcott, who has seen his progress hampered by a string of niggling fitness issues.
"I am 21, so I want to play games every week now, it is a big season for me.
"I have been very unlucky with injuries last season and I am looking out for myself a bit more now.
"I am one of the last to leave now, always staying behind after training, practising things . crosses and set-pieces.
"It is down to me, so I will look after myself and am raring to go now."
Walcott's hat-trick was his first for Arsenal, having netted a famous treble for England in their World Cup qualifying victory away to Croatia during September 2008.
Summer signing Marouane Chamakh also got his account up and running with a late header, while Robin van Persie was, along with captain Cesc Fabregas, brought off the bench for the last half-hour.
Wenger sees Walcott eventually developing into a central striker's role.
For now, though, the 21-year-old maintains: "I will happily play anywhere for Arsenal - there is a lot of competition up front now with Marouane and Robin, so as long as I provide goals and pop up with a goal now and then I'm happy with that.
"But if the boss wants me to play up front I'm buzzing from that. I am working in training up front so I'll go from there."
Arsenal briefly topped the fledgling Premier League table on Saturday, before champions Chelsea chalked up their second successive 6-0 victory of the new campaign.
Walcott, though, feels if everyone can stay out of the treatment room, then the Gunners will be a force to be reckoned with over the next nine months.
"We have so many fantastic players and as long as we keep them all fit, we are going to be very strong," he said.
"However, we will not get ahead of ourselves. We want to be winning these games and the most important thing is how we react to Blackburn next week, an early kick off.
"They are the games we need to be winning, the games that might have let us down last season so that's where we will show our characters."