you're on the right track. A "new to you" bike with debris in the tank requires attention to the entire fuel system....tank, petcock and carbs.
Beyond simply replacing carb parts, there is more. Establishing the present vs. factory jetting spec, eliminating previous "mods", fully servicing the oft ignored float system....meanwhile cleaning components restoring factory original clearances.
Assure the petcock screens are present, disassemble (both front and rear sections) and assure passageways are truly clear.
The 250 allows access to install the inline filter, as @
DannoXYZ suggested.
But it all depends on the baseline...adequate fuel reaching truly clean correctly setup carbs. And these 250's especially sensitive to valve clearances. Correctly serviced spark plug wires, terminals within caps.... it ALL works together and all requires revue on that bike new to you. Eliminate any inherited errors or deficiencies.
Frankly, I'd start with a valve clearance check, then working outwards.