I got some news for ya: you are going to be sounding like a foreigner no matter how hard you try. The Spaniards will find it charming and attractive and that will be a point in your favor so I wouldn’t worry.
Let’s see if I can get the rules right because as soon as I write them I think of a word which doesn’t follow them
Single initial Rs are always rolled: rato, reto, rito, roto, rizo, robo.
Mid-word Rs (this is driving me nuts as I try to think of examples and deduce the rules)
After L, N, S, R, it rolls: alrededor, Enrique, perro, error. Robo (theft) is rolled - antirrobo (antitheft) is rolled.
After B, C, D, F, G, K, P, T the preceding letter forms syllable with the r, like in English: Brasil, crack, drama, Francia, grande, Krazy glue, presente, tránsito.
After a vowel: not rolled: araña, arena, arisco, erótico
After H J M Q V W X Y Z ( I cannot think of any examples but let’s say not rolled)
So, I would say an initial R or one following L, N, S, or R are rolled and the rest are not.
El Perro de San Roque no tiene rabo porque Ramón Ramírez se lo ha robado. (All rolled) This one is used to tease kids and all those who cannot roll their R’s. The French sound quite pathetic substituting a gutural sound. And while we are talking about tongue twisters, here’s another tongue twister (from Latin America). Try saying it fast. English ones are easy by comparison.
Compre poca capa parda,
porque el que poca capa parda compra
poca capa parda paga.
One I like in English, not so much because it is difficult, which it is not, but because when you say it fast no one knows what the hell you said:
What noise annoys a noisy oyster most?
the answer:
A noisy noise annoys a noisy oyster most.