How far in advance to book air?

As you can tell, the Midwest is often not the best place to fly to Europe from. Chicago doesn't have many European budget airlines flying into there. Your $832 round trip is not bad, but it's not great either.
Airfares are very much like a crap shoot, and who knows what the airline analysts are going to do after the first of the year. I would think with the economy doing pretty well, there will be quite a bit of traffic to Europe through late Spring and into the Summer of 2020.
You might want to sigh up with AirfareWatchdog.com or one of the discount airfare websites and see what the trends are going like on flights It doesn't take long to get a feel of good and bad airfares.
We caught a $437 flight to Berlin a few weeks ago, but a couple of weeks later our next door neighbor caught a $365 round trip to London from the Mid South. We were both prepared to do a quick buy when those airfares showed up online.
And to answer your question, I'd be looking to buy tickets 90 days ahead of your departure.

Nobody has her crystal ball available. 😉

I got my round trip tix between JFK & Zürich in late summer for my mid April 2020 trip because Delta announced a huge sale & I took advantage of it.

At this point, find an airfare you can live with and buy your tix because as we get into the new year, fares might increase.

I assume you have to fly to and from ORD to your remote Midwest city. That makes it a bit more difficult because the price is higher because of the domestic flight.

Mobile passport can help reduce the time for immigration and customs back into the USA. Unfortunately, it won’t improve the politeness level of the employees.

Is Aer Lingus an option? You’d preclear USA immigration and customs in Dublin and get off at Ohare as a domestic flight and not in the remote Terminal 5.

I’d probably wait a bit. Early May is my usual annual European trip and I tend to book it in early March. Obviously, anything can happen with airfares, but I’m thinking you might do better than the $832.

Your going to get a lot of different opinions on this subject, here is my take. Flights open up around 220 days before the actual flight date, I have made it a habit to look at the fare the moment (Literally) they open up and have found that during the first 24-48 hrs you can get a very good price, then the prices tend to go up to what ever level there going to be til 6 weeks before departure then they only go up from there. I have noticed that sometimes the cost will vary for a few hours sometimes but you have to be ready to jump on them because an hour later they are back to the norm. My way of buying tickes doesn't always work because sometimes you don't plan a year in advance to take a trip. I can't wait till I retire and don't have to submit vacation requests months in advance because then my wife and I can watch the cost of flights and if a really good deal shows up during the last 48hrs we can have our bags packed and jump on the plane for a spontaneous adventure!!

Most important! Once you book your flight don't keep watching the prices because it will drive you crazy!

Are you returning through Chicago and then flying on to your home airport?

Just a warning that the people movers to get you from the International Terminal (T5) at ORD to the domestic terminals are still out of service, so you have to take a really slow bus service (with a really long wait in a really long line). Hopefully they will have the system back up and running by May but it will be nearly two years by then!!!! (In response to your question as to whether that is enough time at ORD — normally it would be, no problem, but the shutdown of the people movers has made it a whole different story).

The price for your flights looks good though.

When you find a schedule and price you can live with, pull the trigger and do not look back.

The super low fares (< $500] are usually winter promos. May is now part of high season so super low fare are unlikely.

There is no magic time to purchase airfare. That may be a good price for your market, especially if it includes luggage and seat selection. You can keep following prices or you can decide this price is within reason and purchase. The choice is yours.

Follow 3 or 4 date pairs for the next 3 weeks and buy if they drop 10% or more. If not, buy at the end of the period and don't look at prices again.

barbwild, if that's $832 for round trip to Rome, that would be a very good fare from Kansas City. What site are you looking at and are you on a tour on which you could fly open jaw - that is, does it start in Rome and end in another major city?

$832 round trip from the remote midwest is good, I would buy it if you are ready (financially and set on your dates). Yes, it could drop more...but it could also increase a whole lot. I tend to have good luck buying pretty early, but there is no magic formula or anything you can use to predict what will happen.

1) not knowing your airport forces lots of generalizations
2) consider not only the cost of the fare but the
2a) total trip time - air time plus layovers
2b) number of stops
I only do carry-on so we don't have to worry about checked luggage.

Carry-on is a pain if you have to transfer. Consider all the costs of your itinerary as well as airfare - will you depart from a city you want to visit or will you incur the additional costs of travel and staying in a hotel on departure.

Thanks everyone, for all the great advice!

To answer questions ... yes I was planning to arrive in Rome, and depart from Venice. I'm flying from CID, Cedar Rapids.
I've been searching mostly on skyscanner.net. I'm somewhat resigned to the current fare - now working to make sure the connections aren't too tight.
I also read somewhere that it's a long trip to the airport from Venice.
Good to know about the remodeling challenge at ORD!
Thanks again. I really appreciate your time and input.