Here's some of tools we use over and over in making our foamcore party decorations.
Use sharp and fresh blades. Get good ones and change the blade often. A blade that appears
sharp and will cut your hand will often chew the edges of foamcore....can't figure that out but it's true.
Foamcore and Foamboard is the same thing. 3/16" works great for most applications and is sturdy and rigid and stays flat unless you get it wet. Then it bows. If that happens just add a bit of water to the reverse side and weight it down and it will flatten right out.
A straight edge ruler is a must for cutting straight lines. Even after all this time I still don't try to cut a straight line without one. I also use a cork backed ruler that doesn't slide on the foamcore.
Make the circle first with a pencil and then lightly cut around on the pencil line. Don't try to cut all the way thru on the first pass. On the second pass you just stay in the track you've made and focus on cutting the rest of the way thru.
This brand is the best. We've tried the others but we like this one by far the most. It's compatible with the foamcore. It doesn't warp it. You can glue photos or lightly mist a board with it and sprinkle glitter over it.
Don't get one of those mini ones. A regular sized one isn't expensive. Get the 10" glue sticks for it as well and it saves some time. Clear glue sticks have the least amount of actual glue in them. They bond just by melting. Milky white ones are good for most applications and the heavy duty tan ones will glue everything...including your gym shoes if you need to!
One Shot lettering enamel is the best paint there is. It truly covers in one shot and the colors are beautiful. They just came out with a new color called Sublime Green and it's the most gorgeous lime green ever. We also love the magenta that is like a hot pink color. The dark magenta is a great fushia pink. Try this paint and you'll love it. It's worth the extra price it is for the time it saves and it's slow drying qualities that allow you to drop glitter on it and have it stick very well.
And last, but certainly not least....glitter. It should be at the top! We love it and use it every day. Nothing beats the sparkle. It's hard to work with those tiny 4 oz. jars. You need to drop a handful on your wet paint and do it over newspaper and then pour what doesn't stick right back into the jar. If you drop it onto spray paint you have to be really fast. It doesn't always stick too well...especially on those lovely Design Master spray colors which dry almost instantly. Some of the other sprays give you a longer working time but the One Shot lettering enamels can give you enough time to even answer the phone!
I hope these resources are helpful in getting the best results from your projects.