...a partner of the opposite sex. Evolution has hard-wired this need, deep-down. I think it likely that every adult feels it, whichever sex floats his/her boat the highest, so to speak.
Sure, it's possible to live a fulfilling life without such a partner, but I think it's healthy to acknowledge that, right now, certain of your needs aren't being met.
Later in life, I also believe that we might be very selective. As our lifestyles become more established by habit, the partners who might magically "fit" could be harder to find.
I particularly liked the way you put this:
...but wonder what it would be like to share my life with someone and have a few laughs along the way...
I like the implicit recognition that, although you've been married twice before, a new partner would of course mean an entirely new relationship, so new that you must wonder just how it would be. Rather than looking to recapture any particular feelings, you are looking forward.
By a weird fluke, I stumbled upon love just a year after a painful divorce. In what you've just posted, I recognize some of the best of my own feelings at the time. Best wishes for you in the future exploration of yourself--and a lucky someone else, if that be your will.