Yes you need a fermentation bucket. Yes you need a secondary fermenter like a glass jug or carboy or demijohn ... and an airlock ... and a racking cane and tubing ... and a hydrometer. But more than anything you need to do your homework.
I’d *strongly* recommend that, while freezing your sloe berries as I note below, take that time while they are freezing to read up *at length* online about how wine is made.
You need to understand what you are doing more than we can write here ... and as well, sloe is not the simplest wine to make decently.
If you are looking for shortcuts ... make grape wine successfully from store bought grape juice (or even grapes) to understand how the process works (google a recipe for grape wine made this way). Then move on to something more difficult like sloe.
There are many good websites to read up on basic winemaking information ... a couple good ones are ...
Jack Keller’s website ...
www.jackkeller.net
and Grapestompers ...
www.grapestompers.com
In any regard ... if you are going to go ahead with the Sloe Wine anyway...
I’d think sloe would be a very interesting and ancient wine to make. Sloes are some very ancient fruit. That 5000 year old mountaineer they found some years ago in the Alps on a glacier (known as Otti, or The Iceman ... seen on PBS), had sloe berries in his bag.
At the bottom is a link to a wine recipe ... however, first a few points ...
Sloes must be picked *very* late in the season, otherwise they can be too astringent and acidic. One old indicator is when the birds start eating them in droves ... that is when to butt in and pick them. Also, it is said to pick them after the first or even second frost in mid to late November.
Once picked, I would put them in ziplock freezer bags and freeze them solid for about a week. Then, when you thaw them they will have split their skins and be much more workable, particularly because, by most recipes, you will be removing the pits (stones).
Sloe berries are loaded with pectin. So much so that some jam and jelly recipes actually include sloes in them *as* the pectin ingredient. So when any wine recipe talks about pouring boiling water over them (as the recipe I’ve linked below does) ... personally I would not.
A better way would be to ... thaw out your frozen berries to room temperature ... crush them etc ... heat enough water to very hot “bathwater” temperature and no hotter. Then, pour it over the sloe berries ... just enough water to cover. Then add the pectic enzyme, stir and let sit at least overnight. The wine-must ideally should be kept at 75* degrees or higher overnight for the enzyme to work most effectively.
Then continue on as your choice of recipe indicates.
Finally, sloe wine takes a long time to mature. Expect that you will need to keep the wine stored (in bottles or jugs etc) for at least a year for it to taste decent. This means ... don’t be disappointed if you go thru all the trouble to make it and then it tastes poorly at the time of bottling. I understand mature sloe wine is excellent though.
Assuming you are going to go to the Brewer/Vintner supply, make sure to get the Pectic Enzyme and the Wine Tannin and use as the recipe indicates. I’d also recommend getting yeast nutrient.
As for the yeast, I would go with Lalvin 71B-1122 or K1-V1116.
A Sloe Wine recipe ...
http://winemaking.jackkeller.net/sloe.asp
Other sloe wine recipes can be Googled.
