Before even considering breeding your fish you need to look at whether you have the space to raise the fry and places to offload them to. You won't be getting just a handful - you can get hundreds.
Most goldfish breeders also cull a lot of the fry - would you be willing to do this? What will you do with the deformed fry (a proportion usualy will be born with deformities that will not allow them to live a normal life - it is kinder to euthanise these).
Depending on what species of minnow you have exactly, these would be easier to breed and also more likely to be born healthy. Not to mention their smaller size would make them easier to raise and easier to find homes for afterwards.
Goldfish may need a long period of conditioning to breed and sexing can be tricky if you are inexperienced.
You also need a large tank to house a goldfish so, if you don't have the fish already, you should know that each goldfish should have 20 gallons to itself (actualy the guideline is 20 for the first fish + 10 for each additonal fish but common/comet types eventualy need even more and fancy types can usualy work in 10 gals per fish).
With both species, the parents are likely to eat the eggs. With the minnows, you should be able to use a layer of marbles to prevent this (try reading up on breeding danios - same sort of thing). You may not be able to do this with goldies which get big enough to swallow them.
Realy, you need to first look into whether you have the equipment and time required and homes for the fry. Once you've done this, do a www.google.com search, search this forum and also check out this site which I have found to be very informative as far as breeding goes:
http
/www.bristol-aquarists.org.uk/index.htm
More specificaly:
http
/www.bristol-aquarists.org.uk/goldfish/info/info.htm
...and also take a look through their links section.