I'm sure there are people who can do a much better job of this, but here goes, off the top of my head.
The main "pre-war" fighter for the VVS was the I-16. This was an open cockpit monoplane, with retractable landing gear (IIRC, the gear were raised manually
) Realising that war was on the horizon, the Soviets went to work on creating Modern fighter designs.
The three of consequence were the Mig-1, Yak-1 and Lagg-3.
The Mig was designed as a High alt fighter, and as such it was wicked fast. However it was a beast to fly, and way under-armed.
The Yak was a decent enough fighter, however it was underpowered, and paid dearly. The design was improved into both the Yak-9, and Yak-3 which went on to become very good fighters. (The Yak-7 was in there was well, however this was originally designed as a trainer, later adapted as a fighter)
The Lagg three suffered from the same underpower problems, however instead of waiting for a new inline engine, they opted to dump a big bellybutton radial engine into the nose of that sucker. This ultimately lead to the La-5, La-7 and La-9.
I believe that all of these fighters were coming into service when the war kicked off.
-Sik