So I'm not sure if I'm going to be upgrading my account once my trial expires. How much would it impact my success with my horses if I decided to stay basic? I have a busy life and I'm not sure I want to financially commit at the moment. Is it worth playing with just a basic account?

Sam has set up the game financially for you to continue to play as a basic with little issue. You will lose the Enter All ability in shows and your other perks, but financially you will be able to keep up.

 I've only upgraded once lol. I've almost always played on a basic account, you lose enter all, which in my opinion, makes it harder to keep up with a large amount of animals. However, as long as you enter shows for the week, and since other players sell tickets, it shouldn't be a big issue to be successful. Although I know you get a 1.5x show points for your breed  specialty if they place in the top 10 for shows, but I don't think that makes too much of a difference.

But you should be fine :) I'm a busy person so I stay basic for that reason, I still keep up financially. (I could probably be more successful if I kept up with training lol) Hope this helps!

first make sure to sell your tickets before you loose the basic, also you can make your private shows and either sell spots or the whole thing (whole would be best in your case) that right there will start you with a good chunk of change.

keep your animal count low.
train every week and they will hit 1mill no problem
also some upgraded players still hand train (no enter all) 
you can see if shows are unflooded and enter them verse enter all where it random chooses. You can still get really good points from unflooded shows
also make your public shows every week and set the price for 3k, you make money off that. 

Yeah! What already has been mentioned above!
You are also still allowed to participate in Mod/Admin/Club run contests which helps with gaining points for your animals or hpd to keep that bank going even if you have a basic account. :)

You all have been so helpful. I definitely won't be upgrading for a while so this put me at ease. Time will tell if I will be able to stick with it long enough to justify spending real money.

I know it's sort of repeating what everyone else has said, but you can definitely play as a basic! The entire basic game is available to you as a basic player. We've been trying to make it easier for basics recently, too. (And if you go down to basic, we'd love to hear if you have some suggestions for how we can make the experience better for new players!)

There are certainly perks to upgrading, mainly in more ways to make game money, easier/higher pointed training, and free cash shop credits. Plus you can upgrade for 6 months for about the cost of going to a movie, so it's definitely worth it when you're ready!

However, I don't want to push you, I totally understand if you're not ready to spend real money - but definitely think about the starter pack which is available to you for your first week! It comes with a 1 month upgrade, 25 mill HPD, and a pair of pointed horses or dogs for $5 USD. You can find it on the Upgrade page if you want to!

I also want to say that you should sell your dog tickets and create your extra public shows (upgrades can make 2 horse shows and 2 dog shows per week!) before your trial expires because you will want that extra money! Also make sure to collect your bank interest if you haven't yet because upgrades also get more interest per week on savings :).

So someone actually just gifted me a large sum of money. I would consider taking the starter pack, but I would feel kind of guilty since I don't need the money now. 

Definitely don't feel guilty! It's there for new players and you are a new player :).