Min-raising from early position with 44
I have mixed feelings about the preflop play. Let's compare the various options
1) Folding Preflop
I don't think it's too wrong to fold a small pocket pair in early position. It just plays really poorly postflop
2) Raising to 3-4 big blinds
My preferred option in tighter games at small stakes (NL25-NL100). We rarely get more than one caller and it's much easier to win in headsup pots with the Flop continuation bet.
At microstakes, I think the average player is much looser and even if you open to 4BB you will often get 2 or more callers. And we can't really bluff on the majority of boards with only 2 outs to a set of 4s.
3) Open Limping
I am usually against open limping, especially from late positions or mid position. But I think it's a decent option from early positions in a full-ring game. As mentioned previously, Option 2 isn't too good for looser and more passive games.
The cons of open limping include getting raised by aggro players. But this isn't going to be a huge issue when the entire table is passive in general.
4) Min-Raise
This is the "in-between" option of 2 and 3. I also think a min-raise is less likely to get reraised, as compared to a limp. I think it's an acceptable option, but make sure you know why you are picking a particular option.
Postflop: I may c/c a small bet or just c/f. Nothing good comes from playing this hand. You have the bottom end of the straight and the board has a possible flush too. Best case scenario is when you get it in against a draw, and most of these draws have at least 2 over cards and a flush draw or open ender straight draw. These draws have 40% equity vs your hand. Vs the other made hands, your hand is completely crushed.