...I went on a 25ish mile round trip cycle from Beith to Largs today. The cycle there was really good, it was all uphill and very challenging (for me anyway). I was looking forward to the cycle back however my rear derailleur broke about 1 mile into the return journey. Nightmare!...
Sorry to hear that, but don't despair as you're probably better off without it; although Simplex had a long history and a great reputation, by the Eighties they had been going downhill for some time. I bought a bike with a
SX610 GT which promptly exploded into the spokes, so you're in good company!
Period Shimano mechs, such as Teuchter referred to, are plentiful and reasonably priced; assuming you won't be going 8 speed, then you have a huge choice. As a beginner you would be well advised to stick to Shimano or Campagnolo, so as to avoid any complications.
There used to be many more component manufacturers and it was quite common for one company's product to be rebranded: you might think you had avoided the woeful SX610 when you bought a Gipiemme Cronosprint, when they are one and the same.
Another reason to stick with the two most common brands, is that the Seventies and Eighties was also a period of great innovation and there are some weird and wonderful bits floating around that will have you pulling your hair out.
Although it's not likely to be an issue with your set-up, now would be a good time to familiarise yourself with two points to consider when choosing a rear mech: chain wrap and sprocket (the rear cogs) capacity.
Sprocket capacity is simply the largest sprocket it can handle. Using
the SX610 GT as an example, you can see (listed as
Max Cog Size) that it can handle a sprocket with 36 teeth, which is pretty generous by today's standards.
If you look at a mountain bike (which tend to have larger sprockets than road bikes) you'll see that the cage (which contains the two jockey wheels) is longer than that typically found on a road bike, so that it can cope with the bigger sprockets: the longer the cage, the greater the capacity. The advantage of a shorter cage is that changing gear is quicker and crisper, hence the different versions.
Chain wrap is explained on
this page (third and fourth paragraphs). These days you are unlikely to see the wrap quoted in the headline specs, as modern derailleurs can all cope with what has become the standard range of sprockets and chainrings. But if you are using older kit or have a set-up at the extreme of the usual range (touring in hilly areas for example), it's worth bearing in mind. The SX610 GT could cope with both of the example set-ups because it has a maximum chain wrap capacity of 38 teeth.