Bicycle Mechanics - installing new parts on old bike

I have an old Raleigh marathon 12 speed. 502 frame.
Just had it tuned up. New tires, new seat, clipless pedals.
I have been thinking about getting a new bike.
Thinking Surly frame and build it up.
I realize I already have an American co. brand Tawainese built steel fram bike.
I was thinking of just upgrading the parts.
It now has 27 x 1 1/4 inch tires on it. I want 700 x 32 or 35.
A guy at a local bike shop said it could be done. Will need to lower the brake pads.
I was thinking of bypassing that need by getting wheels with disc brakes.
That should work right?
I also want to swap out the handle bars and get a newer light wider bar that shifts in the brakes.
I want to keep costs low so will keep the gearing and derailers.

one possible major issue
last long ride I noticed that when riding no handed it tended to leat a tad to the right. Rode at a slight angle to keep it straight.

any insight of experiance in this endever would be appreciated

Pulling to one side can indicate a bent frame, misaligned dropouts, bent fork or headtube. Have that checked out before putting more $ into the bike.

Disc brakes are expensive, and require appropriate mounting points that are not going to be found on your bike. Would require a new fork at least - not sure about the rear. Long reach caliper brakes are available (Tektros are good and cheap).


If you want to swap handlebars that is easy enough, but if you want modern brake/shift levers you will have to upgrade most of your drivetrain to make it work. In addition to a new rear hub (which you would get with new 700c wheels) you would need a new cassette, deraillers, and chain at a minimum. The crank may be usable.

So...conservatively..
Wheels $200
Tires $50
Handlebar $40
STI Levers $150
Chain $20
Cassette $50
Derailleurs $80
Brakes $50

My advice would be to either use the bike more or less as it is, or look into getting a new one. A Jamis Aurora or a Surly Crosscheck can both be had for under $1K.