AVCHD is a type of MP4.
And no, MP4 is not a good editing format.
But still, Final Cut X can import AVCHD and play it and edit it. If you're doing a simple project (some cuts, a fade up, a title) then by all means, leave it as AVCHD and just work with that.
But the instant you get into anything processor intensive (filters, color-corection) then you'll find that editing AVCHD is a bit of a pain. To avoid that, tell Final Cut to "Transcode: Create Optimized Media" when you import. This converts your footage to Apple ProRes.
It will use more hard drive space but you'll find you can actually work without having to wait for stuff to happen.
Based on your description, it sounds like using AVCHD will be fine for you. But it depends on your computer. Try it and also try some ProRes. See if it's worth it to you or if you don't notice a difference.
(Extra Note: When Final Cut X converts to ProRes it leaves the AVCHD footage in its folder, so you'll have both versions while you work. Often, after I'm done editing and exporting a final video I'll poke around in Finder and find the ProRes files and erase them. This way I reclaim some drive space while keeping the original AVCHD files. Should I ever need to re-create the ProRes files in the future, it's technically possible.)