Gonna disagree with Texarkana! 
Decide what your needs are, find a trailer that fits them, and then buy something that will safely pull the trailer.
The MOST expensive part of this is the tow vehicle. If you over buy on the tower then you’ll have less to spend on the trailer. That’s just economics (and unless your name is Buffet or Kennedy you’ll end up short
).
First, what kind of a horse do you have? Are you working with a 14.2 Arab or 17h half draft? What amenities do you want for the horse (water tank, mangers, ramp, step up, etc.).
Second, what kind of activities are you going to participate in? If it’s going to be shows in nicely prepared areas then you have one thing but if you you like back country riding and overnights in the woods maybe you’d like something else.
Third, and related to the second, what kind of hitch system do you want? Personally, I’m a “gooseneck guy” as IME it is much easier to maneuver and haul. But that means a truck and not an SUV.
Fourth, what amenities do want for the people? You took care of the horse part in First, above. You can choose from virtually none to full LQs of varying levels of utility and luxury.
Fifth, how much money do you have? Again, if you are “trust fund baby” this might not be an important question; for most of us it is!!! 
To help yourself out, here, sit down with a glass of wine, a yellow pad, and pencil and just write down stuff you think of as you consider the program. You might be inexperienced but I’m sure you’ve read about things and have some ideas. Once you do that you can discuss your thoughts with more knowledgeable friends.
After you pick your trailer THEN find something that will safely tow it. Remember the First Law of Towing Anything: Starting is optional, stopping is not!!! You don’t need a one ton dually to pull a Brenderup. But you do need enough to pull what you’re going to tow.
Don’t pay any attention to “towing capacity” advertised by the manufacturer; that’s a number out of Marketing not Engineering. Instead you must find the Gross Combined Vehicle Weight Rating (GCVWR, sometimes written as the GVWR) of the truck/SUV. Then find the curb weight of THAT vehicle. Then the weight of the trailer you’re going to pull. Do the math and see how much legal towing capacity you now have. Remember that you’re dealing with empty weight to start with and when you fuel up the vehicle, load it with people and gear, the trailer with horse(s) and gear, load hay/feed, water, etc. that you’re eating into your useful load. Personally, I’d limit myself to not more than 90% of capacity. That gives me some “J-Factor” in the event of a difficulty.
This seems daunting but it really isn’t if you step back, look at the “big picture,” and then plot your way forward.
Do this some time before you actually need to buy something so you can think about it and read about it and learn from others before there is any pressure to act.
In summary: select the trailer, select the tow vehicle, load up and have fun!!! 
G.