How forgiving are these limits?

On Marie they are very, very forgiving. I have more than one year left with Marie at almost max level, max knowledge and reputation, only one item left to craft (the Philosopher's stone, which requires an item that I can only get in one specific day later this year), already killed two special bosses, already made an Elixir to cure Schea.... I haven't checked the ending requirements but I'm pretty sure I already fulfill some of them.

Generally speaking from my experience with Atelier the time limits are only a problem in two situations:

• You want to 100% the games, in particular if you don't want to use a guide or go into NG+
• You are playing Atelier Totori

Time limits in Totori are rough, the only game I had to reload an earlier save because I ran out of time and could not get at least a "good" ending. It's still one of my favorite games in the series though.

Worth mentioning that Marie also does have an "unlimited" mode you can choose at the beginning, but given how forvinging the limit is it's probably not necessary.

And what do you suggest I play first Marie Remake or Ryza?

Between those two, Ryza.

Marie is cute and fun game, but it's lacking in depth compared to other entries in the series. If it was $20 it could be an interesting entry point to the series, but for $10 more than what they're asking for that game you can get a far more complete experience by going with one of the recent games like Ryza or Sophie 2.