Traditional parties are the best! I used to do them for my kids - and their friends, now 6th form age or above - still talk about what fun they were.
Don't over-complicate your plans or catering arrangements. They're too little for anything complicated in the way of games; many of them won't have been to a party like this before so expect to explain the rules. Keep it fun and fast moving; nothing too serious. You can always have joint winners for something and move on if you sense that attention is waning.
Musical Statues is a good one, Musical Bumps, Dead Lions for calming down. Pass the Parcel is a must, but one layer per child and make sure everyone gets something.
If you run out of activities, a disco dancing competition with sweets for everyone at the end, or a "pretend to be an animal" session (you shout it the animal) and they have to mime it).
Maybe set up a craft activity table in a side room if you have space - nothing messy, stickers are good - think of it as a chill out zone for anyone who gets overwhelmed.
Move any precious or breakable things out of reach will make it easier for you to relax. If you're worried about carpet or soft furniture you could get a huge decorators dust-sheet (and tape it down so no one can trip).
Have some basic first aid - ice packs for bumped heads etc.
Plan on 15 minutes of free play while people arrive, 20-30 minutes of games, 30 mins of eating and then maybe another15 mins of games before people leave. 90 mins is more than enough for tiny ones.
Keep the food simple. Jam, cheese, ham sandwiches on white bread, sausages, few different kinds of crisps and biscuits (you can't have a party without chocolate fingers and party rings!) and some cucumber sticks and fruit - maybe halved grapes or hulled strawberries - as a concession to healthy eating. You'll throw most of it away. Don't do jelly and icecream (so messy!).
Have paper plates or pre packed boxes and a bins bag handy to clear it all up quickly afterwards. Get the other mums to help with these kinds of tasks.
Small piece of cake goes in the party bag. Set the most capable mum on cutting and wrapping them while you finish off the party.
It will go super-fast, I promise and you won't know what you were worried about! And you'll save a fortune compared to hosting a softplay party.