The smallest rod that can chuck a streamer or wooly bugger is going to be a 4wt. The size of trout you're referencing would be suitable for a 4wt or a 5wt. A 5wt has the backbone to chuck things into the wind a bit better and also to toss bass poppers of the small/medium size.
Most of the rods sold today are very biased in favor of large western waters (9' length) or to be used for nymphing (fishing with a bobber by a fancier name)
If it were me, I would look for a 8.5' 4wt or 5wt if you're just fishing your ponds. If you think you might want to fish small streams for brook trout as well, I would look for a hard-to-find 7'6" or 7'9" 4 weight.
As to what brands and what "action", most of the rods today are way too stiff, known as fast action rods. They are harder to get the feel and to time the cast than a moderate action rod. Moderate action rods are most often fiberglass and can be much more affordable than the carbon fiber high end "fast action" rods.
Reddington makes a few nice glass rods that are under $200. Don't buy a travel rod that comes apart in a million pieces, a 2-3-4 piece rod is way easier to work with and won't come apart all the time.
Vintage cane rods can be a wonderful thing as well. Antique Orvis bamboo cane rods hold their value and are very durable compared to other cane rod types. A fine antique will cost you $500-$800, LESS than their top of the line, soulless Helios carbon fiber rod.
For flies, you want some poppers, dry flies, and a lot of wooly buggers. For tippet, you want 3x, 4x, and 5x. You want a Weight Forward (WF) or Double Taper (DT) FLOATING fly line.