Having speed I think also gives you built-in options without needing a magic item. As a Wood Elf, you already start at a speed of 35. At level 2 you get an extra 10 feet of movement increasing your total speed to 45. That means you can Dash for 90. Combined with Step of the Wind, you can Dash for 90 or Double Dash for 180 then tack on a double jump at the end. There's a lot you can do with that kind of movement and it will increase even more at later levels.
If your speed is 45 you could move, dash & bonus action dash (Step of the Wind) to go 135, not 180. A dash allows you to move your speed so you would cover 45 for each which is 135. Also, a jump does not allow you to exceed your movement. So if you have already covered all of the distance that you can, a jump will not increase this.
PHB p.190
On your turn, you can move a distance up to your speed. You can use as much or as little of your speed as you like on your turn, following the rules here.
Your movement can include jumping, climbing, and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However you’re moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.
After re-reading the movement rule and the Dash Action rule, I can only come to the conclusion that you are correct. Base Movement of 45 increase to 135 feet maximum when taking a Dash Action followed by a Dash Bonus Action including any jump. Interesting that I had a DM allow me to move 180 feet plus jump in an AL game. I will discuss this with him for future reference.If your speed is 45 you could move, dash & bonus action dash (Step of the Wind) to go 135, not 180. A dash allows you to move your speed so you would cover 45 for each which is 135. Also, a jump does not allow you to exceed your movement. So if you have already covered all of the distance that you can, a jump will not increase this.
PHB p.190
On your turn, you can move a distance up to your speed. You can use as much or as little of your speed as you like on your turn, following the rules here.
Your movement can include jumping, climbing, and swimming. These different modes of movement can be combined with walking, or they can constitute your entire move. However you’re moving, you deduct the distance of each part of your move from your speed until it is used up or until you are done moving.
I'm starting a campaign and one player has a wood elf monk, likely going Way of Four Elements. We're going to flavor the elemental abilities as derived from dragons, so he's channeling raw draconic power. In any case, it feels like there are very few magic items suitable for monks. Does anyone have recommendations?

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.