If you are looking to do a decorative carpet on the stairs (only) then one way to do it is to use the carpet as a RUNNER...not a stringer-stringer carpeting. The other thing to consider is normally the stairs should match "something". If you have different carpet at the top of the stairs that does not match the stair carpet, that NORMALLY means you have different carpet DOWN stairs. The stairs will match the carpeting on the MAIN floor. I'm not hearing that this is your scenario. What type of flooring do you have on the main floor? This is what the stairs will be MATCHING if you choose to go this route (stairs not matching carpet upstairs). The other way to do this is to use the decorative carpet on the stairs and then pay to have an area rug cut and bound in your chosen "stair" carpet. This area rug then sits in the entrance/bottom of the stairs. This is a quick, easy (slightly less expensive) way to get the stairs to match "something".....'cause they really should match something. Right now they match the upstairs carpet. Once you change this design feature, you need to REPLACE it with another version of "must match something". The bound area rug in the same carpet is one of the fastest ways to do this. Good luck. Remember to look at your main level flooring and decide whether or not you want to go forward with this concept.

We've been in the stair runner business for about 22 years. We've found that newel posts, particularly in a very old home may be so wide in relation to the staircase that they complicate the placement of the stair runner. That is, centering it - in a case like that, we often just hug the post with the runner allowing it to be centered on the remaining stairs. In some cases we have cut the runner material around the post - had we not the runner would be completely off-center on the remaining stairs. StairRunnerStore

The way your front door jumps guests right into the stairs, I think iron would be a bit prison like. I would leave the spindles as they are and see what a difference the railing and treads will make. If it isn't exciting enough for you, perhaps new art there would add interest you're looking for. Looks like those two dinky little ceiling lights in the entry could use an upgrade too.

The code has specific requirements for winder stairs. I consider them to be an accident waiting to happen and I avoid them unless there is no other workable alternative. Installing the rail on the side where there is full tread depth encourages use of that (safer) portion of the stairs. I'd relocate the rail, but insurance agents might suggest leaving where it is and increasing your liability coverage as the preferred alternative.