Hi Arcos and welcome to our forum. You'll find a welcoming place here among us. And you've made a good start by asking questions. Help and assistance as well as comradeship is what we offer.
I love your idea of turning Grape vine for bottle stoppers, very apt.
However I can't help you with your first question, I've seen them as I pull the plastic cork of course but never seen the plastic for sale. I shall watch this answer with interest (and maybe a little research).
Your second question I can help with, although all thoughts are personal, others will have different ideas and answers.
I'm assuming you are talking about one of those sub £20 sets of cheap turning sets. Your right, they are not much good for protracted use, to start with you'll spend more time sharpening them than using them. They don't hold their edge and are fairly soft as far as tool steel goes and as you've discovered.
So a Bowl Gouge. Yes you can do more than turn bowls with them. But again the flute can affect the way it cuts. Steep flute walls (a Vee shape) will clog if given a swept back grind but works well with a standard 45 to 55 degree grind. For a swept back (Elsworth/Celtic) grind you need a superflute and almost everyone will say the Henry Taylor is the one to go for.
For the work you are considering I'd suggest the 3/8" but don't try the full swept grind to start with, it can be a bit tricky. Sweep back the wings no more than 3/4" and to allow detail work probably nearer 55 degrees, this will give you a tip for reasonable detail work and the wings for cutting and shear scraping, it will also be strong enough for roughing out small diameter timbers. No it will not be as good as a dedicated spindle roughing gouge, detail (spindle) gouge and skew but if nothing else you'll master tricks that will stand you in good stead for the rest of your turning.
Now the problem is can you grind a swept back grind. If not a simple jig can be made from scraps, take a look at this one for example, but there are many other versions as well.
http://www2.woodcraft.com/pdf/77B61.pdf