The BBC Micro is a special computer because it introduced a generation in the UK to programming and it led to the creation of the ARM processor that is almost universal in mobile devices. It was also the inspiration for the amazingly successful Raspberry Pi - which has a model A and B just like the BBC Micro to show its roots.
The 6502 may be a simple CPU, but getting it right so that it can be used to run real software is still a big problem. There are bugs in the hardware that are often made use of by anti-copy and security code and these have to be emulated if you want commercial code to run unmodified.
Then there is the small matter of timing. The code running in the emulator might well check to see how long an instruction took as judged by the way other peripherals change state. Matt Goodbolt's article describes how attention to timing was all-important for most software protection - read the article for the fine detail.
Of course, a machine is a lot more than just its CPU and we are promised more about the screen and peripheral emulation in a future part.
You can try the emulation out at jsbeeb and once you have it running you can use all the BBC Micro commands and you need to know that F0 is F10, the Break Key is F12 and the "star" key is on the 2 key or the @ key. There is a disk image supplied with one of the most famous games on the BBC Micro - Elite. To run it enter *Elite3 and follow the instructions.
Of course you could always download the code from GitHub and install it on your own server.