I'm still kind of a newby myself, but i would say the bare minimum for building with foam is as follows.
Retractable utility knife. like this one,
https://www.amazon.com/Soft-Grip-Sn...ts=p_n_feature_keywords_browse-bin:2799009011 . Doesn't have to be anything fancy, but the extra blade length and better grip help out a lot for long curved or straight cuts in the thicker foam.
A heat gun, again doesn't have to be fancy. You can spend anywhere from $15-$100. Just get whatever fits your budget. I think i paid around $25 for the one I've been using.
Hot glue gun. Now, here's where it pays off in the short and the long run if you get a halfway decent one. you don't have to spend $100 or anything like that. but maybe go a grade or two above the $8 one you can pick up just about anywhere. Oh and get the longer refill glue sticks, they're worth it in my opinion.
A cutting mat. This isn't necessary if you have a work bench that you can scar up with all the cuts you'll potentially be making. but if you're using a dining room table or a desk like myself they'll save you a lot of headaches and worrying about ruining good furniture lol. Get the biggest one you can afford, they range from 12inx12in all the way up to something like 36x36 or even bigger. Or, you could possibly get a pre-cut piece of "hard board" or something like that from your local home improvement store. Whatever suits your budget or convenience.
Sewing pins. These help me a lot, to kind of pins things in place to make sure it looks and fits okay before attaching pieces together permanently. You can also use something like painters tape or double sided tape if you don't fancy the pins. They do poke tiny holes, but you cant really see them unless you've had a lot of trial and error in the same area lol.
Here is a picture of the first thing i ever made out of foam, just a few hours (maybe more than a few) after acquiring the few things I've suggested.
I just realized that that's not exactly a great photo lol. Not much a picture taker. I was happy with the result and fit the way i wanted it to.
I hope this helps. Please let me know if you have any questions regarding anything I've mentioned, or anything else. I'll answer what i can
- - - Updated - - -
Also if you're after any kind of strapping and buckles like the ones I've used. You can usually find some in the camping section of a big box store like Wal-mart. By the hiking backpacks and canteens and stuff.
