I would certainly advise dedicating a sizeable portion of the time to relaxation and the pursuit of recreational aims. Assuming you manage to gain a TC, prospects for such opportunities will be limited in the future (bearing in mind the PQE structure etc.) so see as much of the world as you can now. Three years of a law degree is tough and with the LPC and training contract (followed by decades of thankless work!) to follow, recharging and refocussing is a great idea.
With regard to paralegaling, I believe that most reputable firms tend to prefer LPC grads for these positions (the shortage of TC's leads to plenty of persons willing to take such work). However, if you can find something it may be deemed beneficial (but would probably require a substantial time commitment). The work of legal assistants is often tedious (not saying that the legal work isn't either...), and I would personally be more impressed by evidence of wider worldly experience and initiative than photographic recollection of the standard form contracts you have slaved over photocopying ad infinitum.
Within the commercial legal sphere exposure to financial institutions etc would aid in the portrayal of possessing sound business acumen and I personally found it extremely useful to have a solid understanding of the basic principles of finance and banking prior to beginning my legal career.