Is the new Jimmy record a good one to start with for that band? Never listened to a full album from them.
Biggest ones for me today are The Almost and The Goos.
That is really hard to say. Part of me wants to say listen to Clarity first but at the same time that album is not always the easiest to get into if you did not grow up with it.
Damage is Jimmy Eat World doing what they do best but I would say Futures or Chase This Light would be the best start. Invented is a really good album that got mixed reviews but probably I would listen to that one last after the band has sank in. Bleed American could also be a start but its also their poppiest and most "pop punkk-ish". Futures has a great mix of rock songs and memorable mellow tracks while Chase This Light is a cohesive pop rock delight that is hopeful and well written. Futures and Chase This Light contain the songs I will always remember best than Bleed American and Clarity that are polar opposites but core to the band's sound especially later on. Invented and Damage are similar to a degree in the fact they are more stripped down rock music with lots of mellow moments. Damage actually is a lot less mellow than some give it credit but overall their last two albums are a fusion of all their known sounds stripped down. Invented was a more obvious example of them doing call backs to previous core sounds from past albums while Damage is a more subtle merging of the best parts of their last 3 albums. Hope that helps.
Edit: The biggest factor to consider is when you listen and what mood since that is how I always gauge their albums. Futures is moody, Clarity is chill, Bleed American is bombastic and a summer rock album, Chase This Light is hopeful, Invented is a reflective record, and Damage is just what they wanted it to be, an adult break up album.