Adjectives in fact "only" have 12 (or 13) different forms with a completely uniform pattern for all the adjectives with no exceptions and (yay!) no stress shift. Feminine paradigm is the easiest to memorize (-ая for Nominative, -ую for Accusative, -ой for everything else). Now, "spelling rules" do affect that pattern (otherwise you would need to learn quite a bit more).
All of the forms are important, but in case you cannot fit them all into your head that fast, start with neuter/zero-ending masculine declension and feminine declension patterns (брат/стул/гвоздь/окно/море, река/мама/папа). Pay attention to Genitive, as it is the most often used case with a very large number of constructions and some twenty prepositions governing it. If you don't get it, you certainly "can't go any further". Besides, for zero-ending masculine/neuter nouns Accusative case (direct object, as in "I wrote a letter") will be the same as either Genitive or Accusative. Now, you learn Accusative for feminine - and you can use all these nouns as direct objects. Then there are zero-ending feminine nouns, which have only three different forms. Then tackle the rest of the cases and the plural paradigm in the order you see reasonable, depending on the texts you use. After all, you can always apply brute force and just memorize the declensions in a week or so using some specific words in flashcards as an example. Genitive plural is the only one significantly harder, as its paradigm has more variation than one would expect. And, yeah... stress patterns are not as straightforward as declension patterns.