As one getting married in June -- I still say go with the traditional wedding. It works, that's why it's been being used for so long. But, if you're going nontraditional...try a different type of engagement ring, something different entirely like a different type of gemstone, perhaps your better half's favorite, with a white gold ring -- which is has a different shine to it, and looks nice with a darker stone. Other options for alternate engagement ring/gifts? I've got nothing.
In terms of the ceremony, if you don't want to do the traditional church wedding -- there are still some interesting ceremonies you could have. Such as a wedding in a secluded wood with only a few close friends/family witnesses; a destination wedding at a tropical location right on the beach with the only witness being the person performin the ceremony; at sea on your own boat, a rental boat, or while on a cruise -- if you're into that sort of thing -- remember, captains can marry you while on their boat at sea and it's legally binding as far as I know; or...in the most random idea I've ever had, you could perform a guerilla wedding -- where you tell you hire someone who can legally perform the ceremony and have them show up without telling your better half one day at random and just on the spot get married -- wherever you may be -- be it in the road, at a restaurant, at the top of the Empire State building, whereever...it would make for an unforgettable random location...or pick a sweet location like the place you first kissed or first met.
Just some ideas, hope they're helpful...