Yes, getting tickets in advance will allow you faster admission. Can't speak to which day of the week is better. We arrived at 3:30 pm, which gave us plenty of time to see everything well before the 6 pm closure. The afternoon light was beautiful, although we were there on June 1; might be different at end of Sept. Yes, double check their Sept hours on the actual website https://claudemonetgiverny.fr/en/ I just looked; last admission is 5:30 pm with a 6 pm closure.
If you decide to take a morning train from Paris earlier in the day, you could visit Musee des Impressionnismes in the AM, have lunch at their nice brasserie, and visit Monet's garden at 3 or 3:30 pm when it will probably be less crowded. Another advantage to going to that museum first is you can buy a combo ticket, which would mean you wouldn't need to reserve your Maison de Monet ticket in advance. (Check hours/days of operation for museum to be sure this is a viable option: https://www.mdig.fr/en/) It's a lovely, small museum (only 3 galleries, if I recall), and nicely complements a visit to Monet's house.
The village of Giverny is small, compact, and very walkable. You could do all that in one day, but it will be a long day. Or, you can just plan for an afternoon visit to Maison de Monet and head back to Paris. I will add another plug, which is that after Monet's house closes, the village gets noticeably more quiet and feels like a quaint village. You could consider having an early dinner in Giverny (I recommend Hotel Baudy) before heading back to Paris. Not sure how that will fit with the train schedule, however. (We spent 2 nights at a B & B in Giverny, just up the hill from Monet's house, which made all of this more feasible and less hectic. I realize you'll be doing this as a day trip from Paris.)
Seeing both the Orsay and l'Orangerie on the same day could be a little taxing. Better to divide them into 2 days, if possible. And you will definitely want to reserve those tickets in advance (they may still offer combo tickets for those museums). VERY long lines for peeps with no tickets at l'Orangerie in May 2023 for our last visit. We were glad we had reserved tickets, and it was quite crowded.