Unusual/Rare Openings for white?

Imho your best choice would be Van't Kruijs 1. e3. That's a seriously underestimated opening.

https://www.chess.com/forum/view/general/underestimated-van-t-kruijs-reversed-french-and-nimzo-indian-attack

Otherwise, U could start with Anderssen's 1. a3 and play reversed openings. A helpful hint (for daily chess): use databases in the reversed sense (ignoring a3 whenever possible and reversing all moves) as if U played with black. In this manner, U can use databases longer than your opponent if he/she uses it in standard way.

Maybe something appealing could be found in Winning Unorthodox Openings by Angus Dunnington (2000).
https://web.archive.org/web/20140708234438/http://www.chesscafe.com/text/hansen15.txt

I've played the Bird's for a decade and had good results.  I've played a3 against FMs.  

I used to play the Dunst (1. Nc3) in serious OTB tournament play. That was when I was rated around 2000 OTB. It can transpose into a number of openings (such as the Richter-Veresov or the Vienna Game) but can also head into unexplored territory.

This line came up a few times in OTB play:

1 b3 or 1 f4 are pretty decent moves for playing original chess.

this is a very good book to get your feet wet and is almost for sure enough for class players to play these openings. if you want to keep playing these lines as you go up higher up the ladder, you should get a book entirely on each individually. :knight on the left for 1.nc3 is the flagship book. theory and practice of the sokolsky for b4,  for b3 you have like 3 books to pick from including one by Lakdawala. ,for 1.f4 you can pick the taylor book or lakdawala's book and so on.

i reckon go for reti, english, 

a simple way to handle white is to play openings like u were black.

1.a3 can make the job, 1.e3 if u are a french player, 1.c3 if u are a Cro Kan player, 1.d3/c3 for a Philidor, etc...

Of all the offbeat openings mentioned above, 1.Nc3 (aka Van Geet Opening) is the best.

Oraguntan opening

Toe

1. g3

The Grob has appeal if you are a sharp tactician; ditto the Amar Opening, Paris Gambit (1. Nh3, d5; 2. g3, e5; 3. f4, Bxh3; 4. Bxh3, ef; 4. 0-O, fg; 5. e4 and so on opening lines for at best very nebulous compensation). If you like solid positions, 1. b3 has considerable charm. Just remember to look up Larsen-Spassky (USSR - Rest of the World 1970) for what to avoid.