1965 ford mustang

There are three types of 289 engines. These are my choices

289/225 HP V8 Engine, 289/271 HP V8 Engine & 289/225 HP V8 Engine ‘a’. How do I tell which one I have?

Don’t you mean 289/200hp v8 as your first choice? That had a 2 bbl, the other two had 4 bbls. The best way to find out is to use a Mustang VIN# decoder, such as this:
http://www.mustangdecoder.com/plates_1965.html

The (rare) 271 hp motor is also known as the ‘k-code’, from the engine letter on the VIN. It had a manual choke and dual points. Take a look at this:

The 200HP 2-bbl V8 is the C-code engine. The 225HP engine is the A-code and also known as the “hi-po.” The 271HP engine is the K-code and is also known as the “high performance” engine. The hi-po and high performance are not the same engine.

Just because an engine has a 4-bbl now doesn’t mean it wasn’t originally a C-code. I have a '67 that came with a C-code that now has a 4-bbl, Keith Black pistons, aluminum heads, roller rockers and a roller cam. But it’s still a C-code.

What I’ve read and seen only refers to the 271 hp K-code engine as the ‘HiPo’:

“A high-performance version of the 289 engine was introduced late in the 1963 model year as a special order for Ford Fairlanes and Mercury Comets. The engine is informally known as the “HiPo” or the K-code (after the engine letter used in the VIN of cars so equipped). Starting in June 1964, it became an option for the Mustang.”

Correct. The 271hp 289 was a special order $800 option that was hard to get. Considering the entire car only cost $2750 and the 225 HP version only cost $200 more than the six cylinder car, few buyers sprung for the “K” motor, which was $800 more than the eight cylinder car…For your $800 you got a forged steel crankshaft, a solid lifter cam, 10.5 to 1 compression and a dual-point distributor. With just a little tuning, these engines put out well over 300 HP which made them unbeatable in NHRA “stock” classes. They could be reved safely to 7000 RPM. The 225 HP motor was all done at 5500 RPM and that was pushing it…These “HY=PO” motors morphed into the Boss 302 in 1969. They were not as sweet as the hi-reving, short stroke 289’s but they got the job done.

In 1967, you could get a GT-390, rated at 335HP, for just $280 extra…The Steve McQueen “Bullet” car…but these were evil handling nose heavy sleds that had a hard time beating the 225 HP cars in a 1/4 mile drag. They simply could NOT get off the line…