I guess it really depends on what you want to do. If you have a firewall, and saving the money means something to you, then I would do that. You can download a firewall program that will be able to offer what you need for protection.
What makes you think ADSL is more secure than Cable? At the end of the day they are both ways of getting TCP-IP traffic to you.
As for choosing most ADSL providers will throw in a modem as will most Cable providers, just find out what package is best for you.
The main plus point with ADSL is that you can shop around different providers which you tend not to be able to do with Cable. Some providers block ports shape traffic etc so you can pick one that doesnt.
The main plus point with Cable is that it tends to matter less the distance from your exchange as most of the Cable network is fibre anyway, at least to the green boxes in the street.
Well if you have a cable connection and a strong firewall on your computer you should be okay.However, i would suggest just going with a modem i mean its not that much of an extra cost its worthwhile buying this.