You'll find Publisher much easier to work in than Word for arranging blocks of text and pictures around each other in a visually interesting way. This program in the Office suite is optimized for designing flyers, handouts, and other documents more complex than regular documents.
Canva is a cloud-based graphic design platform with templates for flyers, posters, social media, and so on. A free account is required to use it. A wide selection of stock illustrations are available in addition to shapes, backgrounds, and fonts. You'll be able to download your design as a pdf to print.
If you're feeling artsy, you could also use this to design some graphics to use in Publisher (or whatever other tool your prefer).
Stick with plain, serious fonts rather than adding cutesy or abstract fonts. Not only are these fonts more readable, they also convey more authority and respectability than "fun" fonts.
Plan on using no more than 2 fonts in your documents: one for the title and subheadings (this one can be a bit bolder) and one for the content (highly readable). Serifed fonts are easier to read for printed materials.
Including an image or two adds visual interest to an informative page! Stick with something small and meaningful -- an image that somehow helps illustrate your topic is better than generic stock art of a happy student.
Also consider if there's any data you can represent in a chart or table instead of describing in words.
A handout for an audience is even more limited in space than a presentation or paper, so you need to think carefully about how to organize your information so that the order makes sense. Strategic subheadings or emphasized text can help draw the eye and facilitate a reader's ability to skim over the handout, which can help them pick out areas of interest to them. Arranging content into clear columns or rows can also help!
It's not strictly MLA, but you might want to take advantage of footnotes to save space.1
1 A footnote lets you have your citations all in one spot without disrupting your writing. This would be most helpful with webpage sources that don't have page numbers for you to associate with specific pieces of information.
If you decide to print your handouts in the library, a few things to know: