First off - Welcome to WMT. It is a good place to ask questions like these.
Long term bulk-aging no, plastic fermenting buckets are not advised, you want glass or something like a better bottle, which is plastic, but different. Also (and probably more importantly), the shape of carboys is to have a very small neck, so only a very small amount of your wine is exposed to the air.
I take a slightly different view of the way to start in this hobby. First two or three kits, buy inexpensive kits ($50-75) make and follow the directions as close as you can. Remembering that hydrometer readings are more important than specific days, in the beginning. This helps you get down the process of making wine, learning the sanitation aspects. Since you have been making beer, this may not be necessary for you, but it gets you something to drink in 3-4 months, instead of the year. Will these be great wines, probably not, but they will at least drinkable, guaranteed. Degassing is the hardest part of doing this and the electric drill attachment helps a bunch. There are two different styles one with two paddles is easy to find, every LHBS sells them, I don't find them particularly useful. There is one that WineExpert makes that has a tripod shaped end to it (three things stick down longer). It works wonders, 5-10 minutes would be a long time for me to use it.
After that, decide if you want to stick with kits, for now or head off to fruit apples, pears, strawberries, blackberries and of course grapes. Also at some point in there take a look on this site and find Daves Dragons Blood and skeeter pee. Two very easy, quick drinkers. Then eventually move into the longer term aging, letting time do the degassing for you.
Good Luck and ask anything, someone will have an answer or an opinion, probably 10 or 12 of us.