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[DesertFox]

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[Elmiwisa]

Huh...I never took serious notice at the title screen. But I guess I could offer my personal opinion as a player:
First and foremost, I think the title screen is among the least important part of the game (together with perhaps the save/load screen and the preference screen). As long as it is not actively hostile to me I might not even notice it.
What I looks for (as a baseline):

-Buttons:
+Start Game: of course.
+Load Game: unless your game is really really short, but even then since Ren'Py provide the functionality for free, why not?
+Preference: I usually need to set the volume and cps. Other options are usually reasonable by default. And of course, this button should lead to a preference page that allow you to change to the very least: music/sfx/voice volume (if applicable) (and make sure they are separated, not a single "sound volume"), cps and automode speed (and also make it obvious to the player on how to make it infinite cps or disable automode speed-before I came around to learn Ren'Py a lot of Ren'Py game never tell me that setting the bar to 0 actually make cps infinite/disable automode, which is kinda unintuitive).

-Style:
I think the style of the title screen should be consistent with the style of the save/load screen and preference screen. These screen are not truly part of the game, so there are no stylistic reason to make them different, and consistency here make things easier to use to say the least. Just imagine if say your computer change style between Windows and Mac every time you switch windows: things would get annoying very fast, even though both style are usable by themselves.
On the other hand, title screen do NOT need to be consistent with in-game style. In-game style should be based on various stylistics and usability consideration. For example, if most of the game involve using a day planner, I would prefer if the day planner have the style of a day planner (for example, make it looks like a todo list) and can be easily use like one (for example, give a variety of buttons on a sidebar that allow quick access to the available actions); and these aspects of style are clearly unsuitable for the title screen.

-Animation:
Neutral Though I think there are some pitfalls to avoid:
(a) Animate the buttons!!! No no no, if I want to chase down the buttons with my mouse so I can start the game, I would play whack-a-mole instead.
(b) Too flashy. It is annoying, it hurts my eyes, and might make the buttons hard to find. Also, it might cause problems with people with certain conditions.
(c) Fail to indicate where you can stop watching it. I don't know whether it is just an obsession of mine, but if I see a long animation, I would wait until the end to see what information does it reveal. So if you have an animation that cycle through all your 100 BG images, each took 10 seconds, then I would probably took over 20 minutes to watch it, only to be disappointed.

-Characters:
I think this all depends on the game style, so this is hard to answer without something more concrete.

Now for bonus point:

-Buttons:
+CG Gallery: get me hyped up on all the CGs I have not get, and let me view the CG without all the other stuff on the interface.
+Music gallery: very nice. Some time after I finish with the game, but I like the music, I would turn to this.
+Scene gallery: a little bonus, but took much more effort to make than the CG gallery, and it might not worth the effort all that much. I can just load the game instead anyway. And if each of those scene come with at least 1 CG, then it can't even be used to help me hyped up about stuff I haven't seen yet, because the CG gallery already did that.
+Character profile: I just love to learn about the characters, even after the game is over. Doesn't matter if the information are superfluous or not. It should only be available by unlocking though, rather than before the game is even played.
+???: bonus stuff after everything is unlocked? That is basically a sweet farewell from the game to me, that also tell me that I really have seen everything there to offer.

-Style:
Integrate the buttons with the background image. For example, a VN about alchemy might make each button a flask on the alchemist's table. Make sure the buttons are still obvious though.

-Characters:
If the game is in 1st PoV with 1 MC, I think this is a good place to introduce the MC, who have a good chance of not being seen again outside of a few CGs.

[LVUER]

Be creative... I don't really know what I'm looking for at title screen. But an interesting title screen and good music can set my mood into playing the game. But I'm already planning to play the game in the first place if I'm looking at the title screen. Anyway, my favorite title screens are:
1. Chrono Cross.
2. Tomb Raider Revelation (and Chronicles).
3. Valkyria Chronicles 2.
4. Vanguard Bandit (this one is not that special, but the music sets the mood and it's one of the first that use real song as title screen music which usually use MIDI song at that time).

[Yomuchan]

I prefer to keep my title screens simple. Name, character(s), small credits. And a clearly accessible menu.

But don't let style get in the way - remember, you're making a game for the masses. Good luck!