Let's talk trailer features....select to meet your apparent current and future needs.
First thing I think of is an "escape" door in the front. Surprising how many times this is handy. Lead a horse in, leave by the door. It's a safety thing. getting crushed/kicked by horse or cow in the trailer is no fun.
How are you going to load stuff...horses only...a rear gate that makes a ramp is handy for loading...horses do get trailer savvy and will jump in and out of the lip. But young horses especially are wary of the lip and loading/unloading without a chute is simpler with a ramp.
Cattle, you will need some sort of chute to guide the cattle into the trailer. They will jump into the trailer given that they are confined from backing up into the chute and refusing to load...this is done by a swing gate of some kind which forces them into the trailer. The rear gates of the trailer are important for cattle...my trailer has two gates which swing back on each side to form a block against the chute sides so cattle cannot get around the trailer. My chute is actually a lane wide enough to drive into and out the other end. Drive in, open rear gates to form block, run cattle into lane and compress them with a swing gate so that they are forced to stay there until they decide to jump into the trailer.
Dividers are key to safety for the stuff you are hauling and during transport. For horses, one down the middle, or a slant is the right answer. All horses or cattle find travel easier if they can assume a slant position in the trailer. Typically, straight across gates are ok for cattle.
Size...you can put 4 grown cattle into an 8 foot trailer space. A trailer with two 8 foot compartments should be more than ample for your needs and pickup hauling capacity. Wider is better for cattle...makes turning around easier.
Always load live stock into the front compartment unless you also have sufficient animals to make a balanced load in both front and rear compartments. Closing the rear gate on cattle which are wanting to escape can be a real problem unless you think about it first....I MUCH prefer the rear double gate rather than a single rear gate...several reasons which become apparent if you only have a one peace rear gate.
For sheep, goats, smaller animals, you still need a chute for confinement unless you are going to catch each by hand and throw them in the trailer. However, the chute needs to be same width as trailer and you back up to it. Else, animals will escape around sides/under gates.
So, my ideal configuration for your multiple critter scenario would be as follows.
A chute as wide as your trailer, split rear gates which open both inward into trailer and outward to form a block, pipes/poles placed behind the rear of horses or cattle can keep them from backing up in the chute and moving forward into the trailer, a 16 foot inside space with a cross gate, escape door in the front compartment, you can build a ramp in the chute to facilitate loading (beware that a poor fit between trailer floor and ramp can cause a broken leg).
Now, given your skills, I implore you to think about getting a gooseneck and putting a hitch in the bed of your pickup which can be removed in a way that your bed is flat and the ball is not ALWAYS there. There are numerous hitches which you can find which do this and you can either have it installed or do it yourself. Yes, a gooseneck costs a bit more, but I've used both hauling live animals using a F150. The gooseneck, IMHO, is about 10 times safer than a bumper hitch. It's not the typical load/driving situation where they differ so dramatically, it is the unusual situations. with a gooseneck, physics works with you, load is increased on rear pickup wheels, better traction, no lift to steering wheels, cattle moving in trailer have far less effect on pickup, panic stop is far less likely to jack knife...I could go on and on. Bottom line, you will be able to carry larger/heavier loads with a gooseneck, with less driver tension and total safety than with a bumper hitch. I venture to say that if you get a bumper hitch, you will ultimately decide you will need a heavier pickup to control the trailer safely. With a gooseneck and "careful" driving with an occasional extreme trailer load, I think you will be able to stay with the f150 until you need something different because it is mechanically unreliable.
Finally, given your skills, you can surely find a used trailer which will meet your needs at a reasonable price.....there are a number of them out there....try craig's list....given that you can do cash, this will work to your negotiation benefit for used, allowing you to get an excellent condition newer trailer for a good price. No need to settle for something beat up.
You have time to hunt for the right thing...and, be aware that once you have the trailer you will find uses for hauling stuff other than just animals. My trailer is wide enough to load a jeep or toyota car into. Has been handy to have that extra width capacity.
OH, yes, for horses, you need a flooring which has a focus on non-skid...many like a rubber composition. Also, need an enclosed front to keep wind/dirt out of horses eyes.
Horses, OMG, horses....you need to study up now on tack, tack rooms, stalls and sheds, feed room, feed protection from varmints, how to build pens which are horse safe, the amount of time spent caring for the horses...and training them, and figure out who your local horse vet is...not all vets do horses...
Horses force you to do things...get trailers, adjust your pickup situation, water troughs, twice a day attention plus whatever time spent training, grooming, riding, cleaning stalls, etc.... I must tell you your "free" horses are not actually free! I do hope that the lady in your life has significant prior experience with horses and is willing to take care of them else they will be a problem, not a pleasure.
Let us know how it goes.