This is the comic Classic X-Men #39 first printed in Nov. 1989; the story is called "Brigg’s Revenge".
The mutant stalker is called Billy Briggs.
Billy Briggs was a homeless mutant living in Manhattan who became
enraptured with Storm. He became enraged when she did not notice him,
even moreso when a rich man accidentally bumped into him and then
smiled at Storm.
Billy followed Storm to Xavier's mansion, where he noticed her
friendship with Wolverine and Colossus. Confronting Storm and
activating his powers, Billy asked Storm to choose a friend of hers
for him to kill. Storm chose Wolverine, knowing his healing factor
would save him. Billy's attacked on Wolverine gave Storm and Colossus
time to defeat him. Wolverine came close to killing Billy, but Storm
called him off; Billy had been through enough already. She sent him to
Phoenix, in hope that she could help.
Powers: Billy Briggs could release energy from his hands. When he activates his power, his eyes glow yellow.