What you're considering is totally doable, but you don't have the right device. My previous device was a Verizon branded Tab 7.7 that I used as my primary phone via VoIP on their LTE network. Overall, it worked 80-85% as well as a cellphone. When I accidentally destroyed it, I replaced it with the N5100, which I have on a smartphone plan with AT&T.
In order to be a practical replacement for a cellphone, the tablet itself must have built in connectivity, otherwise you'd also have to carry around a hotspot device. Dealing with two devices, battery issues, etc. makes that impractical in comparison to just using a smartphone.
There are many VoIP options, and the cost range from free to expensive. It depends on your needs. Most allow calling and texting to anyone anywhere. I can't make specific suggestions without knowing more about your needs, but I'll describe the process. The first issue issue is the phone number and who has control of it. Do you have a number that you're attached to or are you ok with any assigned number. This influences the second issue, do you want an all in one integrated solution like Skype, or a modular solution, which allows more flexibility. Third, is this going to be used across multiple devices and what kind are they. Lastly, how robust/reliable does the setup need to be (ie. is it your primary phone or just something to play with).
I was initially attracted to using a tablet as a phone to save money. Tablets cost less than smartphones and data only plans are cheaper than smartphones plans. Then I quickly got addicted to the screen size. A tablet makes almost every task easier or more enjoyable compared to doing it on a regular size phone. But using a tablet as a phone did have drawbacks. The lack of an ear speaker meant always having a headset readily available (and charged) or using the speakerphone. Most VoIP apps drained the battery rather quickly. Call quality is highly dependent on network latency, no problem on WiFi, more of an issue when out and about.
I couldn't go back to using a regular phone as my primary device. I'm not saving any money by going this route, but for me it's worth the premium to have a tablet with built-in telephony capability on a smartphone plan. The N5100 is an awesome 8" smartphone.*