He understands parties; he doesn't understand PLANNING parties. He thinks they just happen. A lot of kids can't make decisions.
So I would invite his friends. Then I would decide on what kind of party to have. He may well get overwhelmed by huge parties - so scale it back. When our kid was 9, we invited 9 or fewer guests. When he was 6, we invited 6. Do not invite the whole class - it's too much. Besides, I don't want my kid getting 25 gifts! If you have a smaller number, then the birthday child can (and should) open his gifts in front of the guests and they should be able to see his pleasure in opening. Otherwise, the gift is just the "price of admission" to the party, and people think your party is a big gift-fest where the parents try to recoup the cost of the entertainment by raking in 25 presents! Teach your son the etiquette of opening, oohing/aahhing, saying thank you, and putting the gift aside until later. He may not know this, and it may not be what he has seen at other parties. But teach him anyway - he is to be equally appreciative of every gift, say "Thank you for choosing this. I really like it" (no matter what).
Then set a budget. A bouncy house is not cheap (and there have been news reports this past week of them blowing over with kids in them, so parents may be nervous and you'll need to check with your insurance agent). You could do a Pokemon theme with a few decorations and a Pokemon design on the cake. But kids this age aren't always into themes.
Another thing that is making a reappearance is older style party games - sack races (get old pillowcases) and scavenger hunts (9 year olds are able to read the clues), water balloon or egg tosses (be sure to pick up ALL broken water balloon pieces due to bird/small animal hazards), and so on. Go to the library for a book of party games and get all the rules. You can also have the kids wear bathing suits and run through the sprinkler - at 9, they can entertain themselves for a good chunk of the time.
Don't over-supervise, but do decide what your rules are. A lot of families don't allow gun-play, for example (especially now). So if it's outdoors and you have water play, decide about water guns ahead of time. (You might say "no" just to be sure everyone is comfortable.) Then have alternatives and suggestions, but not a ton of organized games for the whole day. Plan on 3 hours for the party - at this age, the parents drop off and come back to pick up. You don't have to feed them all. Pizza and snacks and maybe one alternative for the kid who is gluten-free or dairy-free would be fine.
Inform your son of what's happening but don't give him too many choices. You should be upbeat and confident so that he knows it will be fun.