I am trying to determine which evolutionary model is best for my discrete data using the function ```fitDiscrete()``` from the ```geiger``` package.

These are the values that I get for the number of parameters (```k```), maximum log likelihood (```lnL```), ```AIC``` and ```AICc``` for each model:
```r
     k   lnL        AIC       AICc
ER   1   -115.8006  233.6012  233.6637
ARD  90  -85.98459  351.9692  -303.2308
SYM  45  -97.23202  284.4640  491.464
```
The same dataset (n = 66), tree and single trait with 10 levels were used to create each model.  The only difference is the evolutionary model fitted (equal rates (```ER```), all rates different (```ARD```) and symmetrical rates (```SYM```))

I am having trouble interpreting these results, however.  

To start, for ```AIC```, I'm fairly sure that I should select the model with the smallest ```AIC``` score, i.e the ```ER``` model.  

For ```lnL```, however, I have seen that the model with the "largest value" should be selected with this being interpreted as the value closest to 0 (https://www.r-phylo.org/wiki/HowTo/Ancestral_State_Reconstruction), i.e. the ```ARD``` model.  I realise though that ```lnL``` values tend to be biased towards models with higher ```k``` values.  To address this, I did do a likelihood test as suggested by the website above (chi-squared test), which came to p < 0.001.  This would suggest that the ```ARD``` model should be preferred over the ```ER``` model, which contradicts what the ```AIC``` scores are telling me.

As for ```AICc```, again, the "smallest value" should be selected but the negative sign mixed in with the positive ones has thrown me.  Is this the smallest absolute value or the value value closest to negative infinity?

So, all in all, how can I tell which model should be preferred?