Welcome to the other side of pin ownership: these 20+ year old machines need parts all the time, and you'll soon find yourself with a nice little collection of bits and pieces. Remember that not all bits are interchangeable between Gottlieb Stern and Bally/Williams. You will soon come to know and love the two main UK suppliers namely pinball mania (Andy Netherwood aka the Legend) and pinball heaven (Phil). Everyone has their favourite and I think most of us mostly stick to our chosen supplier but also sometimes use the other one as well. Other UK suppliers include Dave Wilcox (pinball daze) and onestoppinball (John Mel) and there's a couple of others that mostly specialise in LEDs.
You will soon build up a collection of:
Rubbers
Bulbs
Plungers links pawls
Springs
Fuses
Micro switches
Leaf switches
Grommets
Diodes
Nuts and bolts and screws and washers
Sleeves
End stops
Star posts
Balls
Bolts
Plus other assorted crap
Also tools:
Screwdrivers
Sockets (imperial)
Allen keys
Multimeter
Soldering kit and shrink wrap tubing
Needle nose pliers
Magnet on a stick
Level
And cleaning stuff:
Novus 2
Isopropyl alcohol
Foaming cleaner
Maybe some carnuba wax
Microfibre cloths
Cotton buds
Fine grit sandpaper
Metal polish
Sorry to be the bearer of this news, you'll accumulate it bit by bit and it can be fun to learn new skills, I enjoy it a lot more than I thought I would.
For your current needs, you want a Gottlieb flipper link but check the plunger and end stop don't also need attention (take pics, people will tell you). I have all those bits and would happily send you them but am away from UK and its probably better you start checking out the websites: stat with pinballmania.co.uk and pinballheaven.com. The PH website is way better (Andy will admit that his site is pants) but prices and service are all comparable.
Enjoy!