You need a "permit to carry pistols or revolvers" to purchase a handgun in CT.
You do NOT need the state permit to carry pistols and revolvers to own or buy one. If you are moving into the state, you can drive them unloaded, locked up, etc straight to your residence where they can never legally leave UNTIL you get the state permit. You do need at least an "eligibility certificate" (not the same as the pistol permit), which is only good for a short (60 days?) period of time to purchase a handgun and then you can take it either home or place of business IF you're the owner. Seeing as how you have to meet many of the same criteria as getting the pistol permit, it's pretty stupid just to no go ahead and get the full blown permit which allows you to carry concealed.
Interesting fact. If you compare all of the state pistol permit holders to the number of people eligible to get the permit, CT has the fourth highest ratio of concealed carry permit holders in the US. Even higher than gun loving states like AZ, TX and FL. This is not necessarily because people want to carry concealed. If you wish to do ANYTHING more than merely "own" a handgun, you're pretty much required to get the state permit because you can NOT transport a handgun (regardless of condition) in ANY way and without a valid temporary or permanent state permit, you risk a Class D felony. Because of the "regardless of condition" wording, I take that to mean detail stripped, locked in 5 different containers, no ammo even in the car, etc. BELIEVE me...I know this first hand as I have a good ol' southern boy ex-coworker sitting in jail right now because, even though I warned him, he did NOT feel he needed a permit because it was "stupid" just to go to the range. WRONG!!! Undercover state police officer spot checked the range and he got popped with THREE handguns and no permit. I heard he was charged with TWO Class D felonies for EACH handgun. One for illegal possession (can't be outside the house) and the other for illegal transportation of a hand gun.

Don't know what the final outcome was but I bet SIX felony charges pretty damned painful...and expensive. The bottom line is even that little old lady with a .38 snubby in her night stand who NEVER intends to carry a day in her life MUST have the full state/carry permit to legally go to the range once or twice a year to not end up like my ex-coworker.
The laws do say you can transport a handgun (without permit) to a place where "formal training" is to be accomplished. According to Sgt. Bastura (XO of the SFLU), range practice is NOT "formal training". If you get stopped, you'd better be able to prove you're on your way to "formal training" by having your name on a sign up roster or something in writing when returning saying you completed the training and have it DATED.
You can have all the evil features on something like an SKS, because it doesn't have a detachable mag.
The bull-sheeyat thing is I can convert an SKS in 7.62 to take AK-47 mags and put on a pistol gripped non-folding stock and grind off the bayonet lug and essentially have a heavier version of an AK. Same firepower, capacity and perfectly legal. Oh, and there is no ban on magazine types/capacity or hollowpoints. You can have ARs that are not specifically banned by name, like Colt, but, like was was said previously, only ONE "evil" feature with the detachable magazine. Surprisingly, class III full auto stuff is perfectly legal once you go through the hoops. So, a "real" full auto AK-47 is legal, but the semi-auto one in 7.62 is not. I guess CT just relies on the fact that full auto anything is so expensive that it will remain a rarity.
As for defining the "AK type" that is banned... I bought an AK-74 in 5.45 at a gun show in Waterbury and sort of freaked out when I researched the laws after the fact. Again, in email exchanges with Sgt. Bastura, he explained the "three criteria" thing. In order for it to be a "type", it has to meet all three requirements of: 1) Does it "look" like an AK-47? Yup on the 74 aside from the distinctive muzzle break. 2) Does it "function" like an AK-47? Definitely. And 3) can AK-47 parts be swapped into the rifle and make it function? Nope...ain't no way you're stuffing a 7.62 down a 5.45 chamber. So it passes by failing the 3rd criteria...for now. Hope they don't change anything in the future. Again,
One more thing to add... When getting the state permit, you start by applying for the temporary state permit through the police department in the town you live in. Do NOT let them impose ANY extra requirements beyond what the state requires. Many towns require things like three letters of reference vouching that you're a "good guy" and they must include that they know this letter is specifically for obtaining a state permit. You do NOT have to provide these and they are NOT a state requirement. My town asked for them and tried to jack me around. A call to the station from the SFLU straightened that right up. The BFPE FAQs (most of which are no longer there because they were afraid people would take their answers as legal advice - I know because I asked where they went) stated that any requirement beyond what the state needed was NOT a reason for denial of a permit application in any way. Besides, think about it... What's a guy new to the state to do about getting three letters of recommendation? Ask co-workers or neighbors who barely know you to knowingly endorse hand gun ownership? Some towns not only require the letter, but they will follow up and actually call the letter writers, too. Not gonna happen as I sure wouldn't put my butt on the line like that and I'd rather they not know anyway. You cannot use family members for the letters, also. Fortunately, again, this is NOT a requirement and can NOT affect you getting your state permit. Hope this info helps and I do, in fact, live in CT.
Added for those who don't know... SFLU = Special Firearms and Licensing Unit (state police/department of public safety firearms unit) and BFPE = Board of Firearms and Permit Examiners (they issue the permits, do revocations, appeals process).