The rear wheel can change to a 9 speed since you want to swap the cogs anyway. Then you can use a 9 speed shifter.

None of this alters the fact that this is going to cost you more than just selling the old and buying a new bike to do all the mods you mentioned.

But if you're sure you want to go through with it then as LarDasse mentioned the brake levers are a fussy part. You need to find some old canti levers so they have the right cable pull and leverage ratio. But if you can't find any then a newer option that should work are Avid Speedial levers. These use a movable cable stop shuttle to adjust the leverage ratio. When turned in all the way so the shuttle is closest to the bars the leverage ratio should come close to or match the leverage ratio of the canti style levers.