If you've never used a laptop before, you should try one out (any manufacturer) at a store to get a feel for it. Not everyone likes laptops and if you've only ever used a desktop, you might feel like you are being constrained. I don't like laptops for that reason.
Next up, screen size. The 13" screen is a substantial reduction in screen size from 27". Most people do well going to a larger display, not so much the other way around. Especially if you've only been on a larger display. It can actually feel more exhausting to use a smaller display.
A laptop won't charge if the battery is fully charged, so keeping in plugged in is not really an issue. By default, closing the lid will turn your Mac off, so you have to set it to remain on. You must have an external display attached for this to work, otherwise it will turn off. Based on the Apple event, the wake is nearly instantaneous. Of course real world usage may show otherwise.
Once you start hooking up a laptop for external displays, power, et al... it becomes far more cumbersome to just grab and go. Some people like desktops because it forces them to be in work mode when they are at the computer and not in work mode when they leave it. Sometimes having the ability to take your work with you is a blessing other times it's not. Remember bringing those books home to study over break only to have them sit there the entire time until you went back to school? Didn't turn out to be so productive after all.
Based on your workflow and the fact that you have had a desktop setup for so long, I would think the Mini would be a better fit. If you go that route, you will need a display, keyboard, and mouse. If you opt for a laptop but wish to use it at a desk and plan on keeping the lid closed, you will also need a display, keyboard, and mouse.
When getting a display, make sure it will be compatible with your device's interface. The integrated GPU has some resolution restrictions so check out the technical spec page for details of what it will support.