I'm new to the motorized aspect, but not the bicycling part.
My preferred equipment is:
1) flat-resistant tires (Schwalbe Marathon Plus is my bomb-proof choice, but there are others cheaper)
2) old-style glue+patch kit (noxious, flammable glue),
3) Topeak Mountain Morph pump (a folding "floor-style" pump,with a hose to prevent bending the tire stem during inflating)
4) I also like to carry a spare tube that is known-good (either a new tube or a patched & tested tube). The first flat then I can just change to the new tube.
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The Schwalbe Marathon Plus tires above are $45 each.
Some cheaper good ones are the Continental Town & Country tires, they come in 2.1" width.
You need a wrench to get the wheel off, if it's nutted. Something thin+stiff to stick through the tire-hole to push out debris is a good idea too. Bicycle multi-tools usually have something usable for this.
I don't carry tire levers, don't need them. You shouldn't need tools to get a bicycle tire off and on, and they tend to pinch tubes anyway.
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