The phrase "the first type of" is correct and usable in written English.
You can use it to indicate the first of a group of two or more items. For example, "The first type of fish we saw was a bluegill."
Everywhere else, criminal damage was the first type of offence.
"The first type of financing that goes away is new construction financing because it's more speculative".
Ironically, the first type of response is the answer to the second.
The first type of voting machine could have audio functions and other features requiring elaborate software.
Let's call the first type of business Hollywood and the second type Silicon Valley.
Homer's Iliad is the first and greatest poetic account of the first type of war.
"It's often the first type of object a designer works on," says maverick artist Ora Ito.
"Sometimes when the going gets tough, corporate philanthropy will be the first type of philanthropy to be cut," she said.
The first type of policies are typically harder because they often require deeper, more structural changes in society.
"With the first type of error you've just got to flush it from your mind.
The first type of approach is convex ℓ 1 relaxation.
