Your parent's glasses do you well, but the ones you linked to are very different.
It's best to get a mirror and try some on. Glasses are not really divided into male and female styles, that is just a facade to keep glasses-wearing, "pro"-their-own-gender customers happy. Square frames can compliment anyone, in my opinion. It is just a superior shape of frame. I've had round frames, and rimless ones, any feminizing or masculinizing
(is there a better word for this?) effect of the shape is completely imperceptible.
The color and any intricate designs, now that is where the money is at.
Assuming a medium-sized lens:
Wireframe specs will make you look younger/nerdy.
Resin/plastic frames will make you look like a hipster or yuppie.
Somewhat substantial metal frames will make you look somewhat sophisticated or classy, or even just well-read.
For example:

These are somewhat sturdy copper-colored rims from the mens section. Rather than having a masculizing
(
) effect I get more of a naughty librarian look at times.
Another style
(pic taken 7 years ago when I was very macho)
Rimless glasses, they are very light and wiry, but not feminizing.
It's all in how you present yourself, so just get a style that you think compliments your self image.