Welcome to the forum!
If you are on a tight budget, the Shimano Sienna is a decent option for around 30-35 bucks. The Shimano Sedona runs about 60 bucks and is also a good reel, and will obviously be better quality than the cheaper model. You would want to go with the 4000 size in Shimano reels (Shimano reels are numbered 500 to 4000, higher numbers = larger line capacity and stronger drag), or a comparable reel that would hold 120-200 yards of 12 pound mono. The Sienna has a much weaker drag, but if you are running 25 pound mono for salmon it would still be enough.
As far as a rod goes, I would suggest going with an Ugly Stick. They are a decent rod at about 60 bucks. If you wanted to go more expensive you could look at North River graphite rods for 80 bucks (Fisherman's Marine in Oregon City, their house brand) or something like the North Rivers in the same price range. Graphite rods similar to the North Rivers will run 75 to 90 bucks. The Ugly Sticks are fiberglass. At this price point and this being your first rod I personally would lean towards the Ugly Stick.
Higher yet, you could get an entry level Lamiglas G200 series rod which are in the $120 range. Lamiglas makes quality rods, and they are made in Washington. The other rods I mentioned, and almost all rods in this price range and below will be made in China.
It really all comes down to what you want to spend. Going with an Ugly Stick and Shimano Sedona 4000 reel you would be right around 100 bucks or less.
If you wanted to spend 20-30 bucks more I would highly suggest going with a better reel, like the Sedona, not a more expensive rod.
If you had a price of $200 or less in mind I would suggest going with the Lami G200 and a Shimano Sedona 4000, and you would see a large increase in rod quality over the Ugly Stick.
Keep in mind that a spool of good line will be 10 bucks for mono (braided line will be more expensive and adds a whole new level of complexity, and these kinds of things can get overwhelming fast). I would suggest no more than 12 pound good quality line for steelhead and 20 or 25 for salmon. Your drag should be set at 1/3 the breaking strength of your line.
As far as rod weight goes I would suggest a rod rated at 8-15 pounds for steelhead, or 10-30 pounds if you intend to use it for both steelhead and salmon. Those numbers are the size of line you should be using. The action should be "medium" or "medium-heavy" for steelhead only, or "medium-heavy" or "heavy" for steelhead and salmon as well. The action is essentially how much "backbone" the rod has, and how easily it will bend.
I hope that this wasn't too much information at one time. I tried to cover any other questions that might arise. If you do have other questions I'll do my best to answer them.
Be sure to keep in mind everything that others post as well as what I said, and make a decision after you have gathered plenty of advice. There are a lot of people on here with great advice, and I'm sure that other people will have more to add.