1 GHz will do just fine, as the highest freq used by cable is 860 MHz. i think 2 GHz is used by satellite. anyway, you might run into an issue with low levels, especially if this splitter is going after any other splitters. the loss will be 7 dB on each leg. an amplifier might help, might hurt.
the additional through-loss will add 7 dB to the modem's transmit level. if that ends up exceeding about 55 dBmV, your upstream will croak and no internet for you. no, you can't use an amp on the upstream.
stop by the cable company's office and ask for a 4-way splitter, should be free and good. if it makes you feel better, paint it gold and write "MONSTER" on it.