If you've read through that you might be worrying that it's a lot of equipment,
but do remember that some of it (the solder picks and different soldering surfaces for example) are optional,
and what you do buy will last you for years and be used for many many soldering projects!
Essentially all you need are something fireproof and heatproof to work on, tools to safely move your work, solder, flux, something to melt the solder with and a way of cleaning the silver afterwards.
If you have room for a permanent set up then that's wonderful, but many of my students set up temporary soldering stations in their kitchens.
A baking tray with soldering blocks makes a great soldering area!
I've linked to the main supplier of jewellery equipment that I use here in the UK, Cookson Gold, but have a look at this blog post for more ideas of suppliers in the UK and the US.