OK, I'll try without any of the "you don't need a .... to do yeast" adnd give you the stuff I think you should have to do it fairly properly.
I do skip the step of plating to get a pure culture and just go straight from source yeast to slant though. I can cover plating if you really want, but someone else will be able to do it better I'm sure.
Here's what I think you "shold" have. This isn't meant to be a how to thread, I'm just putting in some of the techniques to illustrate why you need the equipment I reckon you do.
Growing your yeast:
To go from a slant to a pitch you need your stirplate and a few flasks/tubes. Your cultures should rise in 10 fold steps for ales and 5 fold steps for lagers so...
For an Ale you go. Loop of yeast -> 10-15ml wort in a little tube -> 100ml wort in a conical flask -> 1L of wort in a conical flask and that will give you about 100 billion cells, or the same as a very fresh Wyeast Pack or Whitelabs tube. From there, you want flasks big enough to go to whatever starter size you want to make. Probably 2L is enough for most reasonable-fairly strong ales.
For a Lager you go. Loop of yeast -> 10-15ml of wort -> 50ml of wort -> 250ml of wort -> 1-1.25L of wort and that gives you about 100billion cells again. And to do lager starters I think you need a 4-5L flask. You can get away with a demijohn, but best for purpose would be a 5L Erlenmeyer. They are poisonously expensive though (up to $100+)
So covering all bases .. you want as an optimum - a small tube at say 80-100ml, a 250ml Erlenmeyer, a 500ml Erlenmeyer, a 1L Erlenmeyer - and then for your "starters" a 2L & 5L Erlenmeyer.
I manage to make do with 1 x 500ml, 1 x 2L and 1 x 5L plus a couple of tubes. But life would be easier and things a touch more sterile with the extras.
To make slants and inoculate your yeast into starters:
A pressure cooker. A small one will do. I think its important to autoclave/pressure cook your slants and direct culturing equipment, simply boiling will do for flasks. If you are willing to pay the shekels for a big arsed pressure cooker that would be better - but even though I said I wasn't going to do the "you can get away with" thing, you can get away with just boiling your flasks.
Small tubes that are autoclavable. I use 15ml screw cap tubes from the bulk buy mentioned earlier in this thread. They are perfect.
Some agar agar from the asian supermarket. Gelatin is to hard to use and melts, you can use it, but agar is better.
An inoculation loop. I use a bit of stainless welding wire bent into a little loop at one end and a handle at the other with some gaffa tape for grip.
A little alcohol burning stove or a bunsen burner .. some sort of flame to make an updraft and to heat the loop
Alcohol to burn in the stove and to make things sterile
some dme.
Making The Slants
Divide your tubes in half - into one half, fill to a little less than the halfway point with wort at 1.030 mixed with agar agar. The other half of your tubes fill to a say 3/4 full with just the wort. Screw the lids on and then back them off so that they would pull off if you tried to lift them. Upright into the pressure cooker inside a coffee cup or something so they dont fall over. Pressure cook them for a while.. to long is no harm, so I just cook the shit out of them.
After the cooker cools enough for you to touch, open the lid and as you take each tube out, tighten the lid. Wear gloves and try to get it done while things are still really hot. The agar ones get laid on their sides to give an angles surface, try to get the maximum surface area you can. These are your slants. The wort ones are just a source for pre-sterilised wort for your initial 10-15mls - its a PITA to try and cook that small an amount up on spec.
For both tubes and slants - keep them at warm room temp for a week before use, so that if anything is going to grow, you will see it and can toss that one away.
All that gets done in advance - tubes and slant will last indefinitely, or at last for a very long time.
Innoculating from a yeast pack onto a slant.
Wear a facemask - I tie a bandana over my face. Light the little alcohol stove and when you work, try to work close to and sort of over the flame so you are in the updraft it creates.
Use alcohol to wipe down the outside of your yeast pack, dip into the alcohol and set on fire the blades a pair of scissors. Cut open your yeast pack. Heat up your inoculation loop in the flame till its red hot, dip it into the yeast pack, wipe the loop on the surface of the agar in a slant. Tighten the lid onto the slant. Repeat for all the yeast packs or slants you want to make.
You should use sterile techniques as best you are able, I wont detail them here as you can google them.
Slants at room temp for a few days, to make sure the yeast starts to grow and nothing else does... then into the fridge at 4C. Re-culture every 4-6 months for best performance.
To use a slant
Flame on, mask on, lid of slant dipped in alcohol, lid of tube of wort dipped in alcohol. Flame loop and cool by dipping into alcohol - drag loop across surface of inoculated slant to pick up some cells, then stir it into the tube of wort. let it grow.
If your sterile technique is good, you can use the same slant again and again. I tend to discard it after one use so I make several slants of the same yeast when I am culturing. If you intend to do likewise, then you can do what I mainly do, which is ditch the loop for getting yeast into wort, and just pour some wort directly into the slant itself.
I think thats it - less than a perfect sterile technique and proper micro people out there are probably flinching/laughing - but its served me pretty well, isn't as much trouble as it sounds and on the scale of "too slack -- proper" I think its on the "proper" side of the balance point.
Warning - you have both highly flammable alcohol and an open flame... do not set yourself on fire. That would be bad.
TB