I'll agree with oldigt...brace yourself.
We have a 7yr old and a 2yr old.
With the 7yr old we had her first few parties at home...never again...lol
If you have carpet...it will get food trodden in it, I guarantee it

For food we served rubbish food (by rubbish I mean nutritionwise).
Sandwiches, cake, crisps (cheesy puffs

), sausage rolls, cheese puff pastry rolls (like sausage rolls but with cheese and onion in obviously). Nibbly food. Kids won't want to eat anything else.
Games wise, you can play pin the tail on the donkey.
We got one from Asda (Pin the trunk on the elephant), and rather than use a pin, we just used blu tack.
We got one reduced to 25p, and got a spare for a friend, but he didnt want it...PM me your address and you can have it gratis
We play musical statues (where, when the music stops, the children have to stand perfectly still...3 yr olds will be old enough to comprehend this).
Pass the parcel (good for all ages), like DS says, with a lolly inbetween each wrapper. Don't need to use wrapping paper. Newspaper for the layers. And you can have presents in the middle layers too. (Good to cheat and gets lots of little presents, and make sure there are enough for each child, then cheat and make sure each child gets a present

)
Musical chairs is another.
Twister isn't too bad, can be had for £5 if you shop around (good for the family too).
Some parents go for the party bag approach. We tend not to all the time.
For a party bag, just nip to the supermarket, and buy a packet of party bags for a couple of pounds, and some multipacks of sweets. They do big multipacks of mini Haribo sweet bags for a pound or two, containing lots of little bags. Lollies too.
Napkins with a piece of cake in too, and as has been said, sometimes a cheap toy. We dont bother because we know the toy will always end up broken or in the bin, so whats the point...lol
As for school, not sure about where you are, but it's customary for the child to take a bag of sweets in on his birthday, and the teacher gives out a sweet to each child at the end of the day. (Same with nursery, as at 3yo I suppose yours isnt in school yet

)
Ooooh paper plates (well, bowls, much more manageable)...jelly and ice cream.
Big jugs of cordial juice, and plastic cups.
I'm also a moderator on a parenting forum with 66 thousand members, so if you need any more advice, I can ask on there if you like, they are great at coming up with ideas for this sort of thing.
Regards
Marcel