What type of time series model would be good? I am trying to fit a time series model to the following data. It seems to be seasonal. Would an ARIMA model be good?

Here is the data:
Count

2
1
4
5
4
8
7
11
4
4
11
7
10
7
0
19
13
13
11
9
8
16
10
12
9
7
21
9
10
6
7
19
18
9
19
15
14
17
9
10
10
13
15
20
15
12
15
16
The numbers are separated by spaces.
 A: *

*delete the leading zeroes as they can inflate the autocorrelation function

*a visual suggest possibly a level shift and then a slight upward trend

*a few anomalies , maybe just one , (pulses)

*no apparent seasonal structure.


An ARIMA model would be good just as long as the reflections above were considered.
If you want to post the data , I will be more specific as to the applicability of ARIMA. 
The 114 values you posted are quite different from your original plot. The actual-fit-forecast is. The acf of the original series shows little structure  . The "best model" contains no ARIMA structure but evidences a few unusual data points and three distinct means or GROUPS [1-32 ; 33-69 ; 70-114 ]  with outliers  . What we have here are three arima models of the form (0,0,0)(0,0,0) with three different means or regimes XBAR1=8.0 ; XBAR2=14.826 and XBAR3=10.8572. One could consider this single-dimension cluster analysis (see Univariate clustering of time series  )
A: It would also help if you set your data as a time-series such as:
1. Make a R timeseries out of the rawdata: specify frequency & startdate
gIIP <- ts(Trimmer, frequency=12, start=c(2005,11))
print(gIIP)
plot.ts(gIIP, type="l", col="blue", ylab="Title of Chart", lwd=2,
        main="Full data")
grid()
