How far can I play with a POD in 1788, if the US was still to be a rising superpower by 1900 (similar to OTL)?
Pretty much as far as you want. In 1788, the major factors leading toward the future superpower status of the U.S. were already established: large land area with ample resources, population with a strong culture of law and civil order, absence of nearby external foes. When starting with such advantages, success is probable even with variant scenarios.
I want to make it so that 1. the USA has similar economic size/political prowess as OTL of that era by 1900, 2. it is filled with anti-British sentiment.
Possible?
Sure. One could use a favorie hobbyhorse of mine: succession to the British throne of Ernest Augustus, Duke of Cumberland, and degeneration of Britain into an oppressive reactionary oligarchy. The PoD could be the death of George III's fourth son, Edward Duke of Kent in 1788, so that he is not around to beget Victoria in 1820.
Better yet, eliminate all four of George's older sons: Edward, William, Duke of Clarence (the third son, OTL's William IV), Frederick, Duke of York (the second son, died 1827, and the eldest son, George (OTL's George IV) in a smallpox outbreak or fire in 1788.
That would make Ernest Prince of Wales and Regent until the death of George in 1820. IMHO, he would be as despised as George IV was. He was much more reactionary and much nastier than William. He would have been Regent and then King for about 40 years.
Then Britain becomes the great leader of reaction in the 1800s, while the U.S. becomes the champion of liberty.
While this might seem like an unequal contest, it seems probably that Britain would have severe internal difficulties that would weaken her considerably. Many if not most of the British people would be hostile to the reactionary government, which would have to devote much effort just to holding power.
Britain might thus lose Canada (which OTL had a serious rebellion in 1837) to the U.S. Britain would probably support Spain's suppression of independence movements in its American colonies; the U.S. would aid these movements, and at their eventual success they could unite with the U.S. Thus the U.S. would be even larger than OTL; almost certainly a superpower.