Hi Angelica,
Regarding upgrading: XP Home to XP Pro are different versions of Windows that come with different features, as you've learned. XP Home is a less-expensive version with fewer features, and generally speaking you would need to pay more for the more fully-featured product if you decided you wanted to have XP Pro instead. (Since you already own one version of the product, you may be able to buy an "upgrade" instead of buying XP Pro brand new. An "upgrade" would probably save you a little money, if one is available. You may even be able to purchase & download the upgrade online, though I haven't checked that.)
However, you may not need to do that if you're willing to use a stand-alone program for remote access, such as those you already mentioned. What you need to do is take a look at each of those services and find out what their system requirements are. They'll tell you exactly what type of operating system you need to have to run their product. Usually they have this under their "Product Information" page, or "FAQs", or a similar section.
For example, I just looked up gotomypc and under its FAQs, it says that the host computer (the one you're going to access remotely) needs to run "Microsoft® Windows® 2000, XP, Vista or newer". It doesn't specify which version of XP, so I read that to say that any version of XP will be fine. But if you want to be completely sure, reach out to a customer service rep and ask. (If I were you, I'd probably do this.)
I hope this was helpful and that I did not just write a bunch of stuff that you already know.

If I did, my apologies! Let us know what you end up working out.
good luck!