Cheese in the Swiss style can be pretty broad, so let's narrow down your goal
Do you want Emmentaler (the cheese with eyes)?
DO you want something more like Gruyere?
Or are you after something along the lines of an Appenzeller?
A good cheese to make to learn the style is Mutschli, it is easy to make and very hard to mess up, and you can eat it quickly. But it has all the basic steps of an alpine style cheese. This is much like Appenzeller, made the same. The difference is only in how Appenzeller is washed.
As for culture, American producers tend to believe Swiss style cheeses should use Lactobacillus Helveticus. Actually in Switzerland they use Lactobacillus Bulgaricus. With the exception of Emmentaler, most cheeses strive to prevent growth of PS (eye former) which is naturally prevalent in the environment there.
You can use yogurt to culture Swiss style cheese. It will work surprisingly well. Something like 1 tsp yogurt per DL of milk should work well.
The basic steps of Swiss cheesemaking are:
Heat the milk to 32 C and add culture and rennet (if using powdered culture, put it in before you heat the milk, and heat it very slowly)
Coagulation time is 30 to 50 minutes. shorter for a cheese you want to age long, longer for a cheese that is softer and aged less (an Alpkäse has a 30 m coag, an Appenzeller more like 45 or 50 m for example)
Then is the 'Vorkäsen' or preliminary cheese making stage, this is where you make the curd.
First, test the gel with your finger to see if it is hard. It's impossible with words to tell you what is right, this is something that is learned. But it should when you run your finger through it stay cut and not ooze back together.
Then turn the top of the curd over, use maybe a small saucer or plate to do this. Just skim off the top and flip it over.
Then with a knife cut the curd into big chunks about 3 cm square.
Take your saucer again and use it to stir the coarse curd, dip it in on the far side of the vat and draw it toward you, this pulls the bottom of the curd up. break it into chunks until it is fairly evenly sized, big huge chunks of curd.
Then with your hard or whisk or whatever you have stir the curd with a 8 pattern until the curd is all about the size of a coffee bean.
Now with a spoon or stick or something, continue to stir the curd, not cutting it. This gives the culture more time to act, and the curd more opportunity to draw moisture and fat out of the whey through calcium bonding.
All of these together, the 'Vorkäsen' should take a total of 20 to 30 minutes
Now we cook the curd, constantly stirring the curd we heat the temperature. So higher the temperature, the harder the cheese and more it can be aged. A lower temperature makes a moister cheese that ripens quickly, but cannot be kept as long (like Appenzeller)
The range here is 40 to 56 degrees normally
We break that into 3 categories:
40-45 is a 'Halbhartkäse' or semi-hard cheese, can be aged up to 1 year, as short as 2 weeks. This would be things like Mutschli, Appenzeller, Raclette
45-50 is a 'Hartkäse' or hard cheese, but on the bottom of that scale. These can be aged 2 months to maybe 18 months. Not many cheeses made in this range, a few types from Central Switzerland.
50 and up is a Hartkäse in its truest sense, this is things like Berner Alpkäse, Sbrinz, Gruyere, and Emmentaler. These ripen very slowly, but are high quality cheeses. In general they should be aged a minimum of 6 months and up to 3 years (Berner Alpkäse can last 10 years) THe longer the age, the harder.
A heating temperature of 50 and up should be reached slowly after 30 to 45 minutes of cooking, stirring constantly.
A temperature of 40 to 45 should be reached after 20 to 30 minutes.
Mutschli is cooked normally 40 to 43 degrees.
A cheese aged past a year or 14 months is often classified a Hobelkäse, or grating cheese as these get very hard and are sometimes difficult to cut. Think like Parmesan.
I have adopted the practice of allowing my cheese to air dry for 1 day before placing in the brine.
A Alpkäse I will leave in brine for 20 to 24 hours
A Mutschli stays in for 30 to 48 hours, depending on its size.
The first will have very little salt. The second will be salty, but not like a Parmesan.
If you want eyes (PS growth) you will have to brine it only enough to harden the rind. Salt will inhibit PS growth.
Then there is also the Raclette. It is made either by removing about 1/3 of the whey. That is replaced either with water 60 degrees to bring the temperature up to around 40 (Berner Raclette), or with water 32 degrees and then the whole heated up to 40 as earlier (Walliser Raclette) This will be a very sweet cheese.
