To address the original question - it depends what you mean by 'established'. I'm assuming that the OP doesn't think we are 'established' and many others seem to agree, largely based on the money we don't spend in the transfer market.

To get a bit of historical perspective I thought I'd throw a few facts into the arena. Palace are the 10th longest surviving member of the top division, last playing in the second tier in 2013. Here's a list of the clubs which have been there longer with the year they last played in the second tier:

Arsenal 1915
Everton 1954
Liverpool 1962
Man U 1975
Spurs 1978
Chelsea 1989
Man City 2002
West Ham 2012
Southampton2012

So in terms of establishment, we're not doing too badly but it's pretty obvious that apart from the big 6 plus Everton there's quite a lot of churn. Basically you need quite a lot of money to guarantee staying in the top division - well beyond anything we are likely to have. So the reality is any match against a team outside those 7 is a relegation 6-pointer - enjoy the ride folks!