I am a non-EU citizen trying to enter Hungary from Serbia by train or bus.
I have a visa type D single entry for Hungary.
My travel plan: From Tunisia to Belgrade, Serbia and then from Belgrade to Budapest.
Will I face any kinds of problems?
Of course you can; the Serbian-Hungarian crossings used by buses and trains are open to all.
Once you're in the Schengen Area, don't leave until you get your residence permit card.