Please recommend a good router for a home computer. I have always used dialup and feel rather safe with it. Thinking of moving up. Not sure to what. I am concerned about setting up a router correctly. Know nothing about them.

If you have a single computer, you won't need a router. DSL or cable modem and network card can handle the connections. Your ISP will generally provide both.
Most routers will include full setup instructions with programs that take you step by step like the wizards in Windows.
Your router will be safer than dialup because it has a built in hardware firewall to protect your network.
To simplify things get a router from the same manufacturer as your network card.

Thank you....I have a number of services turned off including DHCP..I understand I will need to enable it for cable modem. What else should be enabled and is cable best, verses DSL, for a stand alone home PC; also, is there anything I should know concerning security settings throughout my system that would pertain to this/these types of internet connection(s)? This would include firewall configurations.

DHCP will be necessary, unless you pay for a fixed address. This is the service that allows your ISP to set your network address.
When you install your ISP's software it will take care of turning on the services your connection requires.
Security settings can be accessed at the control panel under administrative tools. The majority of these are easy to decide on once you read the descriptions.
One service you might wish to disable is Messenger. A few years ago there was a rash of spammers using this service to send messages directly to your desktop. It is really only needed in a network situation, like a workplace.
Firewalls generally configure themselves. It will drive you to distraction, while it is doing this, by asking about every program that tries to make a connection. This will slow down in time as it recognizes your software.
You will really enjoy the speed of your new connection :) Very much worth the initial hassle to get it setup and running.

Ok !  Thanks dlwolffo..