Following a premade program is not only about having the right exercises, but also the progression scheme, how to handle stalls, and programming in the recovery. If you have all of those down as well, then you'll likely be fine doing your own thing, but if you're new, chances are that you don't.
Maybe it would help if you shared a program that you like but that has exercises you can't do, and we can tell you how to modify it to your needs.
If you don't have any ideas, then some good beginner programs I can recommend off the top of my head are:
- GZCLP
- Ivysaur 448
- Stronglifts 5x5
- Starting Strength
It's fairly complete as far as exercises go, but as you say, it's just a list of exercises. You can build a good program with these exercises, but you can also build an awful one. What are the rep ranges, exercise frequencies, and what's your progression scheme, both short term and long term?
I see that you have access to a barbell. Are you able to do the main compound movements like barbell squats, bench, and deadlift?