I'm just wondering if anybody could suggest bikes to look for seconhdhand wise.
What ends up for sale second hand is so random that, beyond general advice, this information isn't going to be of much use.
As general advice, look for one of the major brands sold at a local bicycle shop (LBS). Also, look at ones that aren't too old (not older than about 5-6 years).
Note that there are some rather good bicycles in the <$400 range. If you have a budget, you should mention that too.
I bought a cheap new bike and to be honest it's been a disaster so I am probably going to go for quality secondhand.
You should indicate what you have and what problems you are having with it.
I use my bike to get to work, to get around the city, and to go on bike rides with half a mind on fitness and half a mind on leisure/fun. I rarely, if ever, go off road, occasionally a mild dirt track or something of that ilk. I don't drive so I also use it to carry stuff such as shopping or anything else I happen to have with me at the time. So that pretty much sums up what I use it for.
What kind of distances? It looks like a hybrid (you probably don't need front suspension), a cyclocross, or touring bike would work for you. Something that will allow wider tires and fenders would give you more flexibility. Check out some of the manufacterer web sites (trekbikes.com) to narrow down the type of bike you prefer.
Comfort, low maintenence, and reliability are more important than speed to me.
Any bicycle of reasonable quality and condition is reliable and doesn't require a lot of maintainence (if it is treated properly). You might need to define what "comfort" means (wider tires will do a lot for that).
I was looking at Dutch bikes on the internet. I like their classic style and they look like the sort of thing I would be after but I wonder how heavy they are.
Expensive, heavy, hard to find used. If you have hills (or want to be able to do hills), they may not have a sufficient gear range.