I've been a Mac user since the beginning - 1984. Since 1984 I've also used the old MS-DOS machines, Alpha Micros, Digitial VAX and Windows machines . . . this just to give you an idea that I used a few different operating systems. I still have to use a Windows machine at my place of employment. Like you, I have a very frustrating time with my work PC, which is on a network with some 8,000 other PC's. Even with a full time IT staff in charge of the server, we get nailed on a weekly basis with all kinds of junk. It's gotten so bad, when our PC's get too bad, they simply install a new hard drive and destroy the infected one, I guess hard drives are pretty cheap now days. With that said, my Mac has never had anything closely related to the problems I have with my work PC.
Yes, I have an Anti-Virus program on my Mac. And yes, I do have a program that scans for Spyware and Adware. The last virus I, or rather my virus program detected was in 1989, which was a MS Word Macro. In the past two years, MacScan has never detected any Spyware, AdWare or MalWare on my machine, which runs 24/7/365 connected to Comcast broadband.
Apple does send out OS, application, security and firmware updates. Via the Mac menu bar, you can automatically check for updates (which I do every 7 to 10 days) and if there is an update, it's downloaded and installed automatically. At most it'll require you to Restart your Mac.
All of the consumer Mac's come with a modem ... although that may change in the future since not many people use them anymore. With the pro-series of Mac's, you will need to purchase a modem.
I currently do everything you want to do, and even more on my seven year old Mac. And yes I running the latest operating system and applications. If you really want to get the full potential of the Mac (or any PC for that matter), you should get a broadband connection to the internet. I've heard good and bad things for both Cable and DSL, so pick which ever is the easiest for you.
I hope this helps.