You are correct, the iPad's built in GPS doesn't function without an internet connection, so you will need a GPS antenna.
That's a bit confusing.
Let's look at the hardware first. The iPad has a combo chip/antenna that does, well, basically everything that has to do with wireless communications. Bluetooth, Wifi, GPS, 3/4G, you name it. If you put the iPad in "airplane" mode this chip/antenna is completely disabled and no radio signal will get in or out whatsoever. That's what commercial airliners want you to do if you are a passenger on their aircraft.
Since this disables the GPS reception too, that's not what you will want to do in a light aircraft, where you want to use the iPad for navigation. So instead you go into the Settings menu and turn off all the radio services individually, except the GPS. (Or, you do as most of us do, and simply don't bother turning anything off.) This means the GPS can now be used by applications. And, like others said, there is NO dependency whatsoever of the GPS part of the chip on any other part of the chip (Wifi, Bluetooth, 3G, ...), with the exception of something called "Assisted GPS".
"Assisted GPS" means that the iPad looks at the 3G towers that are visible, uses these to do a rough triangulation, and then feeds this rough position to the GPS. This means that the GPS is faster in acquiring its (accurate) position. However, assisted GPS is NOT a requirement for the GPS to function. When 3G services are turned off (like they are in my iPad - I only have a prepaid 3G data plan since I rarely use the 3G services) or when a 3G network is not available, it will just take longer for the GPS to get a lock. But once it's got the lock there is zero difference between normal GPS and assisted GPS.
There is one other thing to know about the built-in GPS though. Depending on the aircraft and the exact position where the iPad is mounted/kept, the on-board GPS may not receive a sufficiently strong signal to maintain the lock. In that case you can buy an external GPS (like the Bad Elf Pro and the Garmin Glo), who communicate with the iPad using Bluetooth. This is also the solution if you get the non-3/4G iPad: These iPads do not have a GPS, but they do support Bluetooth, so you can connect them to the Bad Elf Pro or Garmin Glo. (Bad Elf also does a GPS thingy that slides directly into the Apple connector, and thus doesn't need a Bluetooth connection or its own battery or other power source.)
Oh, and these external GPSs don't do Assisted GPS so if they've been turned off a long time they might need a significant amount of time to get a lock. (Absolute worst case, I think, is up to 15 minutes. But that's the scenario where you did not turn on the GPS for many months, and moved to the other end of the world since. They will usually acquire their lock in significantly less than five minutes.)
But honestly, whether you need an external GPS is something you need to try out in your specific aircraft first. I have never had a problem in the aircraft I fly (DR400 and R2160 mostly, with an all-perspex bubble canopy), while others have reported significant problems even if the iPad is kept on the coaming at all times. Only if you get the non-3G iPad can you be sure you need an external GPS.
Next, software. The iPad built-in maps functions all require an active internet connection of some sort (3G or Wifi) since they download satellite and map data "on the fly". In contrast, applications such as SkyDemon, PocketFMS, Air Nav Pro and even TomTom download the maps that you think you need in advance, and do not need to download anything "on the fly". Obviously within the app you need to specify the areas where you're going to fly, and for which the maps and airspace data should be kept up to date. The more areas you activate, the more data needs to be downloaded and stored on the iPad. And in case of some products, the more money you need to pay.
If you do have an internet connection while flying, somehow, then at least SkyDemon is able to download things like weather "on the fly", which may be useful on long flights. I don't know if other products can do this too.
As for your last question, how best to get 3G, well, it really depends on what you want/need. Wifi is pretty much available everywhere. Certainly at home, work and most airfields although you might need to ask around a bit for the password. I personally find I rarely need a 3G connection. So my plan of choice has been a prepaid plan (from Vodafone in my case). It's free until I use it, and then it's relatively expensive, especially when "roaming" in a foreign country. It's possible to buy various day or week bundles, both foreign and domestic, if you suspect you're going to send/receive a lot of data, and that makes things cheaper. But fortunately the amount of data that SkyDemon needs to download weather and notams, and to upload a flight plan is not all that much. To keep the prepaid card active I think I need to load it up with 10 euros each year, and that seems to be about the amount of data I use up anyway, annually.
But of course if you suspect you're going to be a heavy 3G user, then a subscription of some sort, which includes a certain number of GBs each month, will almost definitely be cheaper than a prepaid data plan.
Last, as an "in between" solution: If you already have a smartphone with a data plan, then you can see if you can turn on "tethering". This means the smartphone starts acting as a Wifi access point, router and masquerading device. Essentially this means that the iPad sends out a Wifi packet, which is picked up by your smartphone and forwarded to the internet via the 3G connection. And vice versa of course. This means your 3G data plan of the smartphone is used, and the iPad doesn't need its own data plan.
"Tethering" is sometimes enabled by default by your provider (typically if it's included in your data plan), or you may need to install an additional app. Which, in turn, might require "jailbreaking" of your smartphone.