Maybe a better question would be how do I know if I'm ready to play the Sicilian.
What rating should I be at before playing the Sicilian?

I felt that I couldn't focus on the positional elements of this game because there were too many tactical situations going on at the same time. Maybe I was overthinking it.

For the Sicilian, if you are good at tactics and attacks, it is your opening. Especially the Dragon and Nadjorf variations lead to razor sharp play.
If you want a solid system, study the Kan variation. White can't castle queen-side so there are not many aggressive variations for white.

The day you start playing the Sicilian is the day you stop wearing short trousers.
Speaking personally, the switch to the Sicilian was the best opening decision I ever made.

Learning the Sicilian is important for anyone who is serious about developing their game. One must be patient while learning openings, and with the Sicilian the variations and sub-variations can seem endless. the true benefit of mastering the Sicilian is tournament play.

I'm asking this question because of the game below:
http://www.chess.com/livechess/game?id=752972188
It seems I got tactically overwhelmed and wasn't able to calculate the variations. The move where I lost the rook was just me cracking under tactical pressure. There were just too many things going on at once. How can I simplify the situation when I need to, esp. in this opening.
DarknisMetalDragon, looking at this 30 0 game I see positional mistakes from black (e.g. Giving up dark square bishop for no compensation. Helping to open the position while white has the bishop pair. Weakening several squares.), and nothing tactical there (though I can imagine it was there in your calculations).
For me the question to myself would be : Do I like the positions I get on the chess board, and am I able to create enough joy from it to continue playing this opening ?
If you really like to play the Sicilian, then your rating is simply irrelevant :)
I was trying out the Fishing Pole trap during this game. I probably overfocused on that and tried to play despite the main line not being played for the trap to occur. I focused too much on how to execute the trap instead of watching out for other tactical threats, and the postitional aspects. I think the main move that got me in trouble was the d6 move. He didn't notice the fork the move before, but he could have done it.

For the Sicilian, if you are good at tactics and attacks, it is your opening. Especially the Dragon and Nadjorf variations lead to razor sharp play.
If you want a solid system, study the Kan variation. White can't castle queen-side so there are not many aggressive variations for white.
I play the Kan variation. I am probably worse at tactics than most people at my rating level, but I get by mostly on positional play.

Even Kasparov thought the sicilian was a dangerouse opening. I don't know if you want to play the sicilian so early, maybe your oponents won't be able to exploit your weaknesses, but i think a classical opening (1... e5) will help you more to improve than the sicilian. (I played the sicilian when i was a 1200 player, and i think i didn't improve with this opening)
If you like to fight for the initiative and if you can manage an early weakness from the opening, maybe the sicilian is for you.
I'm asking this question because of the game below:
http://www.chess.com/livechess/game?id=752972188
It seems I got tactically overwhelmed and wasn't able to calculate the variations. The move where I lost the rook was just me cracking under tactical pressure. There were just too many things going on at once. How can I simplify the situation when I need to, esp. in this opening.
Your rating has very little to do with whether you are ready to play the Sicilian Defense. It has to do alot more with whether the opening makes good common sense to you. Do you find it easy to wrap your brain around the idea that Black is going for an assymetric pawn position that creates an imbalance in the position from the very first move. Are you comfortable in unbalanced positions?
I'm asking this question because of the game below:
http://www.chess.com/livechess/game?id=752972188
It seems I got tactically overwhelmed and wasn't able to calculate the variations. The move where I lost the rook was just me cracking under tactical pressure. There were just too many things going on at once. How can I simplify the situation when I need to, esp. in this opening.