I can recommend getting it making a good house with a lift off roof
. The idea being if and when you need to spot clean inside, their nest doesn’t fall apart because you don’t need to take the house out - just take the roof off. And the roof doubles up as a platform for a food bowl eg. If it’s a large enough house to fit a corner litter tray inside, they use it. Then you just take the roof off and empty the litter tray once or twice a week and the rest of the cage stays clean and dry. So you can go longer between clean outs and just spot clean as and when or do the odd things when necessary rather than clean everything all at once- avoids removing all their scent so they get less stressed.
Sorry you probably already know all that!
A shoebox house is a cheap option but might fill up the HH too much. The Ferplast sin guinea pig house is good (no nails or glue - it fits together like a jigsaw and the roof lifts off). It isn’t big enough for a litter tray but then they just choose a corner of the cage and you put the litter tray there instead. Rodipet make great houses with rooms and lift off roofs but they’re expensive. Or just make a long narrow house the width of the cage out of cardboard (like the long house in the Alexander). I find that gives a big house for nesting, a toilet fits inside but it doesn’t take up much floor space in the cage.