Let's assume 15-17 for the range, but all the principles here apply to any range.

Almost everyone now agrees that 1NT should be opened with all 5-3-3-2 hands if in range. I recommend opening 1NT with

QJ876
KJ2
KQ2
A8

or

KQ
K8765
AJ6
K102.

Would I ever eschew a 1NT opening with 15-17 balanced and a 5-3-3-2 hand with a 5-card major? Rarely. Maybe with a small doubleton, something extreme like:

32
AKQJ10
AJ10
432,

but still there will be a rebid problem*.

Speaking of rebid problems, when would you open 1NT with an unbalanced hand? Something other than the expected 5-3-3-2, 4-4-3-2 or 4-3-3-3? Here are some possibilities:

6-3-2-2: A 1NT opening with a 6-card minor (not a 6-card major--never!!) is possible. I'm fine with 1NT holding:

K2
Q10
AJ9652
KQ10.

Otherwise, there is a rebid problem after 1-1M (not quite worth 3, but too strong for 2).

4-4-4-1 to 5-4-3-1: ACBL now allows a 1NT opening with a singleton as long as it is the queen or higher (and the hand is one of the above shapes). Don't go out of your way to do this. It is normal to open 1 of a minor with:

KQ87
K
AKJ65
832 or

K1065
K32
Q
AKJ76.

The only time you might open 1NT with a singleton is to avoid an awkward rebid problem. If you have a hand like:

K
Q765
AQJ
A10876,

you'd be stuck (not quite enough to reverse, but no other good rebid) if partner responded 1 to your 1. So, it is (rarely) okay to open 1NT with that high singleton honor (if the purpose is to avoid an awkward rebid problem). Again, don't open 1NT with something like

AQ54
A
K1087
K765

-- there is no rebid problem.

5-4-2-2: Similar advice to above. Don't go out of your way to open 1NT. Open a normal 1 with

KJ765
J4
A2
AQ87.

Open a normal 1 with

K2
42
AQ765
AQ42

-- there is no rebid problem. If you do open 1NT with 2 doubletons, it is better if the doubletons have honors. 1NT is okay with:

KJ
KQ108
AQ
108765,

but less desirable with:

32
AQJ8
52
AKJ106.

*Definition of "rebid problem" : A problem that arises when all of opener's rebids would be a lie. There is a family of hands that is more than a minimum, but not strong enough to reverse (or jump). There is no way to conveniently show the second suit. The hand contains the wrong shape or range for a notrump rebid (not 12-14). So, each of these hands would be hard to rebid if you opened 1 and partner responded with the dreaded 1:

A
A654
A32
K10765

or

Q
10876
AKQ
A10876.