Welcome to the forum.
Here are some of my thoughts on microscope:
You need 400x magnification for counting cells. That generally means 40x objective and 10x eyepiece. It's also useful to have 1000x but only if you want to take a close-up look. My microscope requires special oil between the objective lens and the cover slide. I rarely use this magnification. These days I actually count at 100x by taking a cell phone picture of the complete fine counting grid of the hemacytomter and use ImageJ to count the cells.
I have the Neubauer style hemacytometer. This seems to be the most popular.
I got my microscope and supplies from Cynmar. The microscope (4x-10x-40x-100x, multiply this by the 10x of the eyepiece) was on sale for ~$160 and has only one eyepiece. Stereo would have been nice, but that was $100 more.
Other stuff you want to get is:
- Methylene blue. This comes in power form and you make a 1% w/w solution that is best stored in an eye dropper. you can use this for testing yeast vitality. Note that for poor yeast vitality, meth blue overestimates the vitality. But I wouldn't use yeast will less than 90% vitality anyway
- get a few serological graduated glass pipetes. They come in handy when diluting samples for counting. Also get a pipet pump. I use just one 10 ml pump for all my 1 ml, 2ml, 5ml and 10 ml pipets. 5ml and 10ml will be most useful for you.
- also get a few glass droppers. They are useful for taking samples
I think that's all you need to hit the ground running.
To quickly determine the cell count in an undiluted sample in a Neubauer hemacytometer you can count the number of cells in 4 of the smallest squares. That number will be the million/ml cell density. For more accuracy you will have to count the cells in a few of the 4x4 squares and use a formula I would have to look up this formula since I have it in spreadsheets. But you can also find it on the internet.
Here is a PDF of the Neubauer grid with indications about the size of the features: http://braukaiser.com/download/Neubauer_hemocytometer.pdf