If it's only the stem that's cracked in your existing bike then it'd be a shame to get rid of it just because you're nervous about doing your own mechanics. Actually it'd be better to fix up the existing one before you go building anything new, because there's less to worry about and it'll be much cheaper - there are specific things that you know you need to change, rather than "holy crap, I need to find All The Parts, buy them, and then learn how to fit them all together".
Stems are easy to change - I did a class with the lovely Nhattattack! and she covered it in the space of about 10 minutes. You'll need to know a couple of things about it (type and size) but you don't need to worry about marks on it to work that out as it should be obvious once you know what you're looking for and you've got your measuring tape out. Check out Sheldon Brown's site for the technical details ( http://sheldonbrown.com/headsets.html ), and have a google for Youtube videos of people replacing them, there are loads of great video tutorials online. Sheldon can probably also help you find the source of the squeak as well.
If you want to buy a new bike anyway (if i were in your situation I'd do both!), it is hard to get a light step-through frame that's also ss/fg. Bikes with one gear are already pretty niche, and by adding the step-through criteria you're looking for a bike that's practically unsaleable commercially. You might have luck buying a complete road bike with a frame you like and converting it to single speed (so mechanical knowledge again), but it hardly seems worth it.
Any particular reason why you don't want to go for a diamond frame?
If it's only the stem that's cracked in your existing bike then it'd be a shame to get rid of it just because you're nervous about doing your own mechanics. Actually it'd be better to fix up the existing one before you go building anything new, because there's less to worry about and it'll be much cheaper - there are specific things that you know you need to change, rather than "holy crap, I need to find All The Parts, buy them, and then learn how to fit them all together".
Stems are easy to change - I did a class with the lovely Nhattattack! and she covered it in the space of about 10 minutes. You'll need to know a couple of things about it (type and size) but you don't need to worry about marks on it to work that out as it should be obvious once you know what you're looking for and you've got your measuring tape out. Check out Sheldon Brown's site for the technical details ( http://sheldonbrown.com/headsets.html ), and have a google for Youtube videos of people replacing them, there are loads of great video tutorials online. Sheldon can probably also help you find the source of the squeak as well.
If you do get stuck, ask here in the mechanics forum and people will be able to advise you: http://www.lfgss.com/forum7.html
If you want to buy a new bike anyway (if i were in your situation I'd do both!), it is hard to get a light step-through frame that's also ss/fg. Bikes with one gear are already pretty niche, and by adding the step-through criteria you're looking for a bike that's practically unsaleable commercially. You might have luck buying a complete road bike with a frame you like and converting it to single speed (so mechanical knowledge again), but it hardly seems worth it.
Any particular reason why you don't want to go for a diamond frame?