Technically my mom hosted our engagement party, but since it was held where we live (2 hours away from her) and we were keeping it really low key, I did most of the coordinating. I'm not positive on the timeline, but we probably got everything together within a month. Because we were going really low key - we just wanted to celebrate and hang out with our friends and family (mostly friends due to DH's family being on the other side of the country) - we decided to go to a bar or brewery. We looked into a few options and found a local brewery that would reserve a space for us for no cost. We worked up a guest list and sent the invites electronically through Minted when they had a free version of their evites. The day before, DH and I went shopping and grabbed an assortment of meats, cheeses, crackers, and fruit for a charcuterie style spread, some water and sodas, disposable/recyclable plates and serving utensils, napkins, table cloths, and a few balloons. I baked cookies, and the day of the party my mom, DH, and I got to the venue maybe 20 minutes early to set up. We made it clear in the invites that we'd provide snacks, and that the party was an opportunity to stop in, grab a beer, and wish us congrats, so there wasn't a massive bar tab at the end of the afternoon. All in all it was a lot of fun, and not too stressful to plan.
The things that made it quick and easy for us were sending invites electronically (even if it meant texting everyone for email addresses), picking a location without a fee or minimum spend, and picking a time between meals where we could just provide snacks.