Do I need to buy the IPad with the cellular option to send and receive texts using my phone number? Or will the wifi only work as well?

Do you have an iPhone - or just an iPad? If exchanging messages with Android or non-Apple devices, you’ll need to use SMS/MMS messaging. By contrast, if exchanging messages exclusively with Apple devices, you will be using Apple’s proprietary iMessage service that operates over a basic network (WiFi/internet) connection.

An iPad, whether a Cellular model or not, is not capable of directly accessing Cellular Voice or SMS/MMS Messaging features. An iPad with either WiFi or Cellular connectivity alone can only access IP-data services. If you have added a DataSIM and Cellular plan to a WiFi+Cellular model of iPad, the number associated with the SIM card is only used to identify your account for billing purposes. This number is not used for making calls or sending messages.

However, when paired with an iPhone, the capabilities of iPad significantly broaden to include access to Cellular Voice and Messaging services of the associated iPhone - relayed to the iPad over WiFi using Apple’s continuity features.

More information about Continuity and the relevant Cellular services can be found here:

Continuity

Use Continuity to connect your Mac, iPhone, iPad, iPod touch and Apple Watch – Apple Support

SMS/MMS Messaging

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding for your iPad on your iPhone...

On your iPhone:

Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

Settings > [Your Name / AppleID] > Messages - set to ON

The iPad, even the cellular model, cannot on its own send texts to non Apple devices.

Any iPad will be able to send iMessages to other Apple devices, and if there is a paired iPhone nearby that uses the same Apple ID, it will be able to send messages to non Apple devices and will appear to them as coming form your phone number as explained in the support document you posted from.

The Cellular option only allows the iPad to connect to the internet, nothing else.

Outside of that, there is no functional difference between sending a message from your email / Apple ID or your phone number when using an iPad.

Whether your proposed new iPad is a WiFi+Cellular or WiFi Only model is immaterial to your ability to exchange SMS/MMS messages with non-Apple devices. To use SMS/MMS Cellular, an iPad of any model is entirely dependent upon an iPhone. A WiFi+Cellular iPad with a Cellular plan can only access IP Data services - and not cellular messaging or voice services.

You may, however, wish to consider other functional differences between WiFi Only and WiFi+Cellular models of iPad. Only WiFi+Cellular models include GNSS/GPS capabilities - which may impact any Apps or features that require accurate and consistent location data, such as Mapping. Purchase of a WiFi+Cellular model does not commit you to using Cellular connections, but provides this flexibility should it be needed.  WiFi Only models of iPad have no Cellular or GPS functions at all.

The absence of GNSS/GPS services on WiFi Only models of iPad is often only noticed after the purchase has been made - sometimes too late to be able to return and exchange the iPad for the Cellular model.

In that case, you don't need to get the cellular model . As long as iPhone is nearby, a Wi-Fi only iPad can send text messages to Android devices just fine.