I presume it is an Ausf F or G. Some earlier models had the aerial in a trough that ran down the side of the vehicle and that should be provided in the kit.
The stug aerials should be 5 cm long in 1/35th scale. The little projection on the later models is actually the mount where the aerial is screwed in, and is still there when the aerial is removed, hence it being on the kit part. In action the aerials would be present, but in transport or in convoy behind the front, they were often stowed. Personal opinion, the models look better with aerials.
To depict aerials I use piano wire which is spring steel (my LHS carries 1m lengths of it @ AUD $2 (about $1.40 USD) which is enough for 18, 5 cm long aerials (allow for wastage). You should be able to locate someone that repairs piano's and find a local supplier). Cheaper than brass, it will flex not bend if you squash it by accident. I drill out the base mount for the aerial and cut a length of wire slightly longer than 5cm - care don't use sprue cutters or you will ruin them; use a pair of wire cutters on pliers. File the end down flat. Then I mark 5cm on the wire and dip the base end in PVA up to the mark to give a little coating for the 'projection' Bill mentions on the mount. Make sure the drilled hole is big enough to accommodate the widened end and glue it in.
Use some fine emery paper to sand the length of wire to remove any oxidisation to help get paint to adhere to it. Paint it Black and Bob's your Aunty.