I own 3 US half cents and I started thinking, I know other countries produced half cents too. So, I've begun a half cent collection of world coins! So far I have half cents from Nova Scotia 1864, British Caribbean territories 1955, Sierra Leone 1964, Liberia 1941, and Netherlands 1884. All were inexpensive and easily obtained. Now I know there are others that will be more expensive and harder to find, but collecting takes time, right?
You might want to consider a Great Britain collection of 1/2 Pennies. I started mine a long time ago and ordered a DANSCO album with the correct sized mm holes to do this. It's an extensive series and a lot of fun. Happy collecting to you.
Sounds like quite a fun collecting theme, and affordable in most cases. Here's a search for denomination ½ + keyword "cent" Some are false hits, but you have a lot of choices, including: British East Indies New Brunswick British East Africa British West Indies Netherlands East Indies Liberia Sarawak Netherlands South Africa Ceylon Rhodesia Netherlands Prison Token! Plus lots more if you consider ½ centimes, centavos, pennies and so on. I highly recommend a ½ Puffin from Lundy. And here are some Japanese and occupied Korean ½ sen (½ of 1/100 of a yen) (Except the top left which is 1/1000 of a yen)
I know that this is the world forum, but here is the first U.S. based coin that had "HALF CENT" on it, the Massachusetts half cent. This wonderful piece came from the Eric P. Newman collection. Here's one that is a bit more affordable. According to "The Red Book" a coin like this should sell for $125 to $200.