Well, George has like 20 different beginners kits. Looking at his most basic kit, you could get by with that and probably even less equipment but you risk less than satisfactory results from the wines. You "could" look for a food grade bucket that is large enough like at a bakery. You don't need a spigot on the bucket, you don't really even need a lid as you "could" cover it with cheese cloth and a rubber band. You "could" get by without a racking cane and just use a piece of hose to siphon the wine to a carboy. You "could" get by with out a carboy and just buy 6 one gallon jugs of table wine, drink the wine and save the gallon jugs for carboys. You "could" get by without a hydrometer if making kit wines and just add a couple days to each step as most kits meet the target SG stated in the step if the fermenting temps are in the specified range. You "could get by without fancy sanitizers and use bleach to sanitize. You "could get by without a bottle filler and just use your siphon hose to fill bottles. You "could" get by without a corker and use stopper bottles or champagne stoppers.
So yeah, you could make wine without any of the stuff supplied in a beginners kit. You risk making a sub par product. You risk contamination of the wine. You risk loosing the money you put out on a kit. You risk added work and frustration. You don't need the "Deluxe" kit if thats what you are getting at. It just makes things more convenient and lowers the risk of ruining your wine. George's Basic Beginners Kit and a corker would get you started on a budget.
I will tell you this though, if you like making wine and get hooked like most of us, you WILL end up buying all of the stuff in the Premiere kits plus some. I started with George's Premiere kit of the time when I started. I use every single piece of equipment in it except the blast washer you can hook up to a spigot to blast wash carboy's and bottles. The only reason I do not use it is I have very good water pressure and the flex hose sprayer on my kitchen faucet works as good. I have bought quite a few other items on top of the premiere kit as my winemaking skills grew and my desire to experiment has grew.
All I can offer in advice if cost is the issue is to either plan and save for what you want or start with a lower level package and plan and save to add to it. Expect extra work to make the wine which could be fun so that is not really an issue. Expect things to go wrong every now and then and messes to occur such as bottling with just a siphon hose. Expect the increase chance for contamination to the wine such as germs from sucking on a siphon hose, using a makeshift airlockand so on.
One last thing I could add is see if you have any friends that might want to make wine as well. Pool your resources and make wine together and share the benefits and results. It could cut down the cash outlay upfront. If you are a regular wine drinker though, the cost of a starter package is quickly recovered if you buy lots of wine as the end cost of a bottle of kit wine is less than buying at a package store or grocery. And remember, the more kits you make, the more savings you gain.
Smurfe