There are a lot of usable trout rods and reels, but I would choose a setup that you can grow into. This is one of the pieces of equipment that will be in your hands all the time, each time you go out. It's an investment that is to be enjoyed!
A small assortment of flies is helpful- use the expertise of local fly shops to choose the best flies for the river and season you are fishing.
No need to splurge on this category unless you want to- choose the organization system for your equipment that works for your style and personality. A waterproof pack for your fly boxes and misc equipment is nice if it fits your budget.
Here is another area in which some equipment can last you a lifetime and some is replaceable each season. Focus on spending your money on good sunglasses and waders, and budget the rest on wading boots, clothing and clothing accessories (in that order).
Any ol' hat will do, just make sure it'll be one you want to wear all day.
You can go for function over form, or form then function. This is a budget area or you can opt for really nice equipment that will last you many years. I have used custom made wood nets from Longdraw Woodworks for all my guiding and I love them. I've also used line nippers from Abel Reels ($$$), but also rocked a pair of fingernail clippers from the grocery store when I started out. My only suggestion in this area: Get a net big enough to COMFORTABLY hold the largest fish you might catch (rubber nets are best). I see too many anglers with tiny nets and it stresses or even injures larger fish when they flop out onto the rocks or are bent so tight in the net that they can breathe or move. Let's keep our fish healthy and strong!