I do like 240mm gyuto and a 150mm petty together. You can always add a cheap serrated for bagels or sandwiches or what have you at first.
You should be able to basically get anything accomplished at home with 240mm gyuto and a 150mm petty. Smaller pairing 80-90mm are good if you do a lot of intricate work or a lot of knife work off the cutting board. if you are not doing that then the 150mm should be fine for small work and using it when you run out of room etc.
I would suggest using some of the budget for sharpening/stropping you need a way to maintain an edge and put an edge back on.
Check this knife out for $125http://www.chefknivestogo.com/kobl2gy24.html
They also have a 210mm for $99.
Then put the rest of the money into like Shapton Pro 1.5k stone and strop with compound. Then when you get more money ad a finshing stone 4k-6k and after that low grit stone 200-500 grit.