The Panasonic HDC-TM60 was a mid-range consumer camcorder introduced in the 2010 timeframe. It captures video at a relatively high compression rate (best quality is 17 mbps), and generally speaking, fast action and high compression do not get along very well - but that is not your reason for the discussion.
For a new laptop, I stick by my original recommendation - any laptop made in the last couple of years with a multi-core CPU and a minimum of 4 gig RAM will do - more RAM and faster CPU is definitely better. Since Playback is not the "lowest common denominator" (editing is - whether only a "little" or not), you need to be sure the computer hardware and software can deal with the high compression and demands of dealing with high definition video.
Typically, laptops are not manufactured to be video editing workstations - and while I understand that is not what you intend or require, you do need to be aware of why... The hard disc drive, CPU and monitor backlight are the major users of power. Typically, the internal hard drives of laptops are made to spin at a lower rate than desktop or external drives because the faster spin means more power use. As well, faster CPUs (even though they do not move) are power hogs. Having more RAM available (jump to 8 gig) will help compensate for the slower drive. Another option is to use an externally connected drive (USB3 - but preferably Firewire 800) for the video project files and edit only when there is main power available (stay aware from editing using the battery in the computer). This way, the computer's memory - RAM and available hard disc space is not competing so much with the operating system for resources.
I don't recall if your camcorder records to MOD of MTS files... but you have the camcorder, so you should be able to know which.
The video editing software included with any consumer camcorder from any manufacturer is basically useless. Even though your requirements are "not much" you would be much better off getting something like the basic Sony Vegas if you happen to to use WIndows as MovieMaker tends to be too rudimentary (even the latest version). iMovie (bundled with Macintosh OSX) is not as full featured as Vegas - but is a good piece of entry level video editing software. Final Cut Express is really good - and costs more than "bundled".
Sometimes you connect the camcorder to the computer and Import or Capture the video when the camcorder is in Play mode. iMovie and Final Cut do this - so not transcoder is needed. Sometimes you copy the files to the computer, transcode, then bring the converted files into the editor. Both ways work, there is no more "correct" way.
According to the manual for your camcorder, the "included software" is "HD Writer". This is not editing software, but a utility that allows copying the camcorder's video files to optical disc (usually DVD). This is not a video editor. If some sort of editor is included, I stand by the previous paragraph. Check the requirements of each of the titles. You want to exceed their stated minimum requirements.
I hope this helps. Obviously, my opinions, only... but if you go in short, expect to be disappointed. If you go in a bit beyond the minimum requirements, you will have a much better video editing experience...