Yes, you can do everything you have described. I'm doing it right now with Verizon and I'm not paying for a texting plan.
The only problem is, if you want to keep using your current number, you'll have to port it to Google Voice. There is a $20 one-time fee to do this, and porting it will cancel whatever line that number was once associated with. So make sure you're out of contract or you'll be charged an ETF. Otherwise, you can get a new Google Voice number (you can pick your number, so you can have it spell something out if you want) and just make that your new number that you give to everyone.
Anyway, once you have a Google Voice number, you will have to set up forwarding. Go to the Google Voice website on a computer, click the settings button, and go to the Phone tab. Then add your phone using your phone's actual number and check the box to have calls forwarded to it. There are other configuration options as well; one very important one is to go to the "Calls" tab and turn off call screening, which is on by default. Otherwise when someone calls you they will be commanded by a robotic voice to press 1 to be connected, and probably most people will just hang up.
Okay, so at this point Google Voice is configured to direct calls and texts sent to your phone number to your Google Voice number. Then you will have to set up the Google Voice app on your phone. Install it and go through the setup. Tell it to use Google Voice as your voicemail provider and to use Google Voice for all calls. That way your Google Voice number will be displayed for all outgoing calls.
You can also call up your carrier and ask that they block all texting to and from your phone. Text messages sent to your Google Voice number will still show up in your Google Voice app. I'm doing this right now with Verizon - no texting plan, about three weeks into the billing cycle I have used zero text messages.