Strawberry plants produce a bigger crown for their second year, so hopefully you'll get a better crop. It sounds as if you have carried out good soil preparation, so a great start.
The main point of using straw is to hold developing fruits clear of the soil, avoiding them resting on the ground or being covered with mud when it rains. Personally I'd avoid using straw, as the only time I have ever done this I introduced loads of weed seed into my plot!
My main problem when growing strawberries is the blackbirds. You will probably have to develop methods for keeping birds away, possibly using netting.