Hey phil,
i have been riding both road and mountain bikes for over 20 years, and have been working in the cycling industry for over 10years now, so should be able too help with a few of your questions.
Post a pic of your bike and i may be able to make some suggestions on cheap improvements, remember a what 20 year old computers and cars were like? well bikes, cars and computers have all come along way.
But in saying that its great you have a bike you can ride and make sure you want too take up the sport again, I will warn you cycling takes away from car time. Its the biggest deter-ant i have from working on my panel van
Maybe set yourself a goal of 2000ks on the old bike and see how you feel before considering a new bike. And if and when you do consider a new bike, purchase that only if you get sized up by someone with the correct skills and tools to do so. I tell customers everyday a good fit up on a bike could make the cheapest bike in the store a better bike than the best bike in the storel if you haven't been fitted too it.
The old diamond back should be fine, id be guessing it was a chromoly frame which would be nice and comfortable but not transfer the power to the rear wheel as well as an alloy or carbon bike. If the diamond back is alloy the power transfer would be great but over longer distances you would get a bit more beat up from the road feel as alloy is very stiff,
This is where carbon ticks all the boxes, light and comfortable, this is why most quality bikes are made of carbon.
The other big difference is gear shifters im guessing your bike would have what we call suicide shifters ( these are shifters that are mounted on the downtube) These are both harder too use and more dangerous.
Newer shifters are mounted on the handlebar levers and these are incorporated in with the brake levers. These make riding much easier.
As for pedals i suggest the shimano r540 road pedal as great pedal that will last and not cost a fortune. and a good pair of basic ROAD shoes, ie the scott comp road road shoe. By goin a road shoe straight away you are eliminating the need to upgrade later, the shoe is also stiffer and offers better power delivery and bike control. A stiffer shoe also lessens the chance of cramping and numb toes.
I use the garmin edge 500 computer, its great and a lot smaller and neater than the edge 800, if moneys an issue and you have a decent phone dload the app, endomondo.
This is a great motivational tool too set goals and see how many kays you have done, it can also tell you you heart rate and how many vertical meters you have climbed. have a look at it its very similar to strava i just found it easier to use.
Let us know how u get on, good too see someone else out on the bike.