The definitive mbed board is the original based on the LPC1768
https://developer.mbed.org/platforms/mbed-LPC1768/It is certainly the best understood board and projects abound. It has really good software libraries and a lot of example code. Yes, I have Nucleo boards with the mbed interface but they just aren't as easy to use.
DO NOT try to install a toolchain until you have used the online tools. You will find that the web interface is PERFECT for developing code although it has NO debugging capability. So, what to do? Use printf() instead!
I have only one major project based on the mbed and I have downloaded the code (and libraries) to compile using Rowley Crossworks. Yes, it works fine and I get the advantage of JTAG programming but, for some reason, I have done all the work on the web version. I like being able to get at my code from whatever computer I happen to have in front of me. No matter where I am. That's pretty powerful.
https://www.sparkfun.com/products/9564When I built my major project, I just installed headers on the project PCB so I could plug the mbed in to the project board. In that particular case, all I wanted was SPI and Ethernet interfaces so the project board was minimal. I really like the 'stamp' form factor when it comes time to wrap things around the outside.