Tbh, you have to take in consideration a lot of factor, being the most important one, In which type of society is he or she inserted in ?
For instance, I can see some pairings working out pretty well in NA, but maybe not that well in a EU society.
Given my experiences, and the fact that i am from EU, this is how i see it.
Aquarius - Probably the best match up overall for a long term relationship with an Aries male. The Aries might feel from time to time like there is some things missing on the Aqua (Aka The Fire), but the broader view of the rship and everything that surrounds her in the day by day (that is intrinsic in her nature as an Aqua), makes this an fairly easy going rship for the free spirit Aries Male (the easiest). They also tend up to be extremely smart (a major point for me). She will provide her love to him not with words, but with actions. Something that an Aries will appreciate to heaven and back.
Leo - The right word to describe this pairing is, treetrunk. There will be a lot of treetrunks, be it up or down. This is my number 1 sexual attraction woman in the zodiac, by far. The Leo woman got this particular thing. Despite her fiery and extreme bitxy nature (on the surface), once she decides to open her heart, what you will see in her heart it's actually very different from what lies on the surface (kinda like Aries in a way). This is the one woman on the zodiac that can really pull out the best that is inside of the Aries male, just by being who she is. Well, given the fact that both can survive the crazyness, that both of them are.
Scorpio - I don't know much about female Aries tbh (like i do as an Male Aries for obvious reasons..lol), but this is the #1 match up that i see with Aries Female. Even with my Scorpio male freinds (the majority of them are Scorpios), when the woman that they are after is an Aries...Ohh trust me, they are completely different. They will shut down immediately and you will clearly see the possessive nature of the Scorpio straight out of the bat hehe It's actualy very funny to see that, because they are always trying to hide who they really are hehe It's very comprehensive on why this match up is so good (imo).
Libra - This 2 pairings inner feminine energies complement each other, pretty darn well. I think it's one of the best opposite matches pairing in the zodiac (M Libra, F Aries). I don't know many couples irl with this pairing so i can't further down my opinion 2 much on it.
For the rest, I think that Sag, Gemini and Aries are also amazing pairings (but maybe not that much distinctive like the other ones that i pointed out). Even Virgo.
As for watter\earth and fire togheter, i can see it working much better in an NA society, rather then an EU one. For instance, Cancer-Aries and Pisces-Aries, can really be pretty darn good matches.