What are the most important excel formulas that the financial analyst should use especially in budgeting and financial reporting?

Functions like  sum, average, count, sumif , hlookup and vlookup are very useful. Pivot & sub-totals will make summarizing data easier and faster. You can use graphs as well for improved reports presentation.

Important basic formulas are Vlookup, Hlookup, sumif, match function

Other might have significant use like index function, Goal-seek function, Average, ABS,indirect, FV 

Pivot Table, Vlookup and Sumif

Nice question, Excel formulas are similar to Lego that can be reshaped depending on a situation. Yet at a basic level to be able to work with Excel at analyst level you should know indexing (advanced vlookup), conditional functions with nested formulas, logical functions. At processing level it is important to work with pivot and data models. Knowing visual basic and macros is sure a great plus. But for a daily basis the above mentioned can help you manipulate data from different sheets and workbooks. At a start, I would advise to build on formulas and learn there different usages especially for Date functions. Hopefully this answered your question.

As far as a financial analyst concerned, There is some intermediate function in excel for the the smooth functioning of financial reports such as VLOOKUP, HLOOKUP, pivot table and graph, $ symbols, Macros etc.. .

There are no standard and it depends on the expertise of the preparer and the size of working papers. In my opinion better are the ones which can help any user to identify the flow of figures, the links for helping the user to reach to the base or data figures.