Replacing an onboard-switch light with a no-switch light will result in the light burning 24x7. You cannot fix that. It is illegal to modify lamps (NEC 110.3).
You're a tenant, so you cannot decide to replace the light. You cannot alter the building: it does not belong to you. The most you may do is identify a light you like, and ask the landlord if it's OK to upgrade it, and then work out division of cost of purchase and installation.
Self-install is out of the question unless a) the landlord explicitly agrees to it, and b) local laws have a "minor repair" waiver that would permit this work to be done by a non-electrician. Needless to say, if there is a pre-existing condition which creates a code or safety problem, or if you botch the job, you are all-in for the cost until the job is done right - either now or at move-out. That seems risky.
There's what you can't do, and there's what you must do.
Light bulbs are consumables, and in a rental unit, you the tenant are required to replace them as they burn out! Fluorescent tubes and starters count. The poor performance of the fluorescent fixture is probably worn out tubes -- Every start, they get slightly more resistant to start, until the starter cannot start them anymore by itself - for a short time longer, they'll work with some sort of little extra "kick". Dark bands on the ends of the tubes are the surest sign of bad tubes. The good news is tube makers have not been idle; they're in a race with LED for best quality light and they're winning. Any tube sold today is 80 CRI; aim for 90 or 95. Looking at the tube, it'll look the same -- but when you look at the stuff in the room that the bulb is illuminating, it'll look fantastic.
It's also possible if the fluorescent has a starter, that the starter is worn out. You can wear it out by leaving it switched on; it will retry starting the tubes 120 times a second. Since it easily unscrews, it counts like a light bulb and it's in your bailiwick to replace it.
There's a small possibility the problem is a fluorescent ballast, especially if it hums, and the timbre of its humming has changed recently. You are not allowed to change ballasts; the landlord is responsible to maintain that part of the fixture. That is the time to sell him on the LED idea (which is a good one).
One more thing. I do not know what possessed you to go off and buy a house part. Plainly a silly thing to do. Wanting to do your own work on your tenant unit is a plain case of "HGTV Fever", you want to own a house, but you don't. Well, STOP No half measures. No kicking tires at Home Depot. No watching home improvement channels (or forums). Go straight to a fee-only financial planner and have an earnest, open-minded, "willing to consider new ideas" and "willing to let go of habits and patterns of belief", soul-searching talk about how to make home ownership a financial reality to you.