Ive never heard of giving straw to guinea pigs - mine just have several types of hay to munch on all the time
I have three cages and i use washable bed pads topped with fleece material in all of them. Reason why i opted to use fleece as bedding is because i found the wood shavings got dragged everywhere - plus it was more convenient when it come to cleaning up their poops everyday - now i just use a small cylinder hoover - takes me about 10mins to do all three cages.
I change and fully wash the fleece every 3-4 days
You can use a shower curtain topped with a piece of fleece for an indoor run - that way any accidents will mean your flooring doesn't get soaked :