Jennifer Hale is considered one of the best (English dubs) voice actors around. It’s almost impossible to be a video gamer without having played one of the games in which she’s had at least one role.
She’s also voiced may animated characters over the years.
She currently has 472 acting credits to her name.
If it helped make the story resonate more with you, sure. But so far as the game plays, the plot progresses, and your dialogue choices are concerned, it doesn’t matter whether you’re playing as a man or woman.
It does change what romantic options are available.
Which doesn’t substantially alter the game. You’re going to be given the same insultingly terrible ending at the end of ME3 no matter your gender.
I usually pick a female avatar (in e.g Mass Effect, WoW, Skyrim, or Dragon Age) and it boils down to pure aesthetics for me.
I know because of the amount of time I spend on character creation screens before ever playing. Even where you don’t get a choice, like Horizon games, what my character is wearing is a big deal to me - I will not always give Aloy the best possible armour ITO bonuses for a given situation, because I consider that set ugly.
I suspect it’s a sublimated desire to be a fashion designer.
Not in a lot of Japanese games. The bishonen aesthetic is quite popular too.
New Vegas, of course, improved on this with the Confirmed Bachelor/Cherchez la Femme perks, which, in addition to the gender-based combat bonuses, allow you to RP a gay/bisexual character and deal with certain situations via same-sex flirting. (Convincing Santiago to become a rentboy as an alternative to paying back his gambling debts is particularly amusing, especially when you report your success.)
I actually think the opposite - Fallout 4’s story fell completely flat for me because the idea that I’d do any sidequests at all if I was searching for my son is ridiculous, and the search for the son story line didn’t land at all for me.
I’m a cishet male, though, and I usually choose female avatars in games, and i don’t even think about it. I have, however, started a renegade run of Mass Effect Legendary, which I never did in the original trilogy, and I’ve started as a guy because I find it easier to be an arse as manshep. Go figure.
My gaming options for doing this are limited but I don’t really give much thought to the gender of the character. It is far more about how interesting they are as I don’t see them as an extension of me in the game.
As was said above, I could see me choosing a female character over a male if the male option was sticking to a boring “grizzled hero” stereotype and the female was far more interesting.
e.g. if the male was a Steven Segal knockoff (and not for ironic effect a la Duke Nukem) and the female was a “Ripley” then I’m taking her every time. (not least because I consider Ripley to be the greatest action hero ever, regardless of sex)
The bolded (mine) brings to mind something, as a cis/hetero woman, I’ve thought about often in my life (I’m fifty-something): I’ve always had a lot of anxiety and angst IRL about the myriad ways I should clothe, adorn, and cosmetic myself up as a woman for socializing/the workplace, and have always joked about my jealousy of how easy men seem to have it in the short hair, no makeup, wash and go with a basic shirt and pants department while being completely socially acceptable and promotable. It’s a more generational view, admittedly, and I assume it’s not so much like that these days IRL, but I have observed a similar variability/lack of in my BF’s games/avatars.
If I let that dissonance bother me, I wouldn’t be able to enjoy 99% of RPGs.
It just seemed… bigger in that game. Even in Fallout 3, finding your dad seemed to be some distant goal that didn’t seem any reason to hurry over. But finding your child?
The way I see it, it’s just a genre convention. Most RPGs mix urgency and sidequests and usually with much higher stakes. Shepherd did some truly impressive faffing about in the various Mass Effect games and the stakes were literally ‘save every sentient creature in the galaxy.’
Personalizing the stakes in FO4 was a great move, but if they threw out sidequests it wouldn’t be an RPG anymore. It would be a standard FPS.
That’s the genius of games like GTA V. Sure, there’s a master storyline, but it’s all more heists and crimes. If you stop along the way to commit even more crimes than THAT, it seems logical.
Dance Dance Revolution for PSX: I tried to spread the wealth between the characters (a purely stylistic choice which had no effect whatsoever on the game), but I found myself gravitating tot he ladies. Not a lot, by about 5-3 or maybe 2-1. I was particularly fond of Workout Suit Emi and Casual Slacks Janet for whatever reason.
Guitar Hero/Rock Band: My create-a-character was always a woman with the darkest skin color possible. I just thought this was a woefully underrepresented demographic in video games. If I made another character, it was a woman with the second darkest skin color possible. I don’t recall ever making a male character.
Assassin’s Creed Syndicate: If I had a choice and it was anything other than liberating a child labor factory (smash way to alarm bell, smash anyone who tries to get to alarm bell, smash anyone still breathing) or a pit fight (smash, smash some more, keep smashing), I always went with Evie. Her skill set, especially her knife-throwing ability, was simply better for the kind of things I had to do to actually progress in the game.
Assassin’s Creed Valhalla: I originally went with the male Eivor, but later switched to female. It made the, ahem, romances a little more palatable, but mainly, from everything I’ve seen and heard this seems like what the programmers actually intended. (I remember Eivor being called “she” in an Order of the Ancients profile.) My headcanon is that the female Evior is real and the male Eivor is how she sees herself… a big, gruff, mead-swilling axe-heaving brute who’d just as soon chop your head off as look at you. So far I’ve yet to see anything to contradict this position.
So that’s my take. As for yours… hey, it’s your game, do whatever the hell you want. 
I would expect that in a game where the main action by the avatar is literally dancing, the aesthetic aspect would be a lot more relevant than in other games.
I typically don’t play female avatars, mostly because they tend to be a bit of male fantasy fulfillment and fan service, and I’m not interested (and find it a bit creepy) to be confronted with ass and boobs constantly like that. And while it’s not a huge concern, I’m not interested in answering questions from my children or wife about it why I’m playing the character with a fur bra and iron thong for armor.
I don’t have a problem with female characters when there’s not a choice- like in Diablo I or II or Overwatch, where there is a mix of male and female characters, each with their own strengths, weaknesses, and playstyles. I didn’t have any issues with any of the female characters except for Widowmaker, who was always a bit too much in the slinky category. Plus I’m typically not a sniper character either.
Well, of course I don’t want Aloy to look like a dumb Nora hick from the Sacred Lands when she visits Meridian.