I just bought this raspberry plant from Home Depot and was wondering if it looked healthy, if i will get berries and, what i can do to protect it from bugs.
Looks fine. What variety is it? That's an awfully small trellis set up you have for what this plant will become.
Minimal trellising can be used on raspberries as they do not form numerous long laterals, and the weight of the fruit per plant is small. Just keeping them upright is enough.
Can't tell if that is a bloom cluster on one plant; berries this year if it is and next year for sure if it isn't.
Protecting them from bugs is a broad subject. Except for cane borers, other bug damage is not immediately fatal and can be assessed and treated after first symptoms appear.
Your motto at present should be "So far, so good".
It is a heritage raspberry and thanks for your input!