Private pilot reported a runway incursion while taxiing to mid point on runway for departure with construction on airport proper. Pilot turned in the wrong direction for takeoff and was stopped by ATC prior to takeoff roll.

Narrative

I turned the wrong direction from the taxiway onto the runway (lining up for 27 rather than 09). This was my fault. The controller told me to stop before I completed the 90 degree turn. I immediately did. After confirming; I returned to the hold short area; reoriented; and he immediately cleared me for takeoff. Thankfully this mistake did not cause any significant disruption to airport operations or safety. Upon climb out; the controller provided a number. I called it shortly thereafter. The controller was helpful and suggested that the airport improve signage to clarify directions for pilots during construction. Additional Details: During a cross country; we stopped in DLH. DLH has significant construction happening on the taxiway. The ATIS contained significant detail but created provision for aircraft with wingspan under 59'. I struggled to make sense of the directions but believed I understood them after listening a few times. I believed I could; in fact; taxi to the end of my departing runway (which looked to be 9 based on winds).After notifying ground that I was ready to taxi; I departed the parking area to the south of the runway. I was instructed to turn right on taxiway alpha which runs parallel to the runway for runway 9. The construction started where I turned which meant I could only turn right. I was going to depart runway 9 and I was taxing away from the start of it. I don't recall any additional signage. [MISTAKE 1: I suspect that I believed I was taxing in the direction that would take me to the end of the runway that I was departing from - but was not. I needed to re-orient myself to the directions from ground] While taxiing; I was asked if I could take off from taxiway A4 and given distance of over 3k feet. I affirmed and turned on A4 to hold short of the runway; and switched to tower. [MISTAKE 2: I was listening to ground directions and complying without cross-checking my map (I had two available) and confirming a plan to depart runway 9. I was mentally preparing to turn back in the opposite direction of my taxi. In truth; this was simple. They were taxing me to the middle of a long runway to take off - rather than having me back-taxi it.[MISTAKE 3: I didn't confirm my orientation with a holding position sign. I should have seen this. At the time of filling this out; I don't recall seeing the sign; but suspect it was there and I was just overloaded on other details.Once cleared for runway 9; I turned left from Alpha 4. I turned a bit wide with plans to do a short field take-off due to a more limited runway and heavy. While turning; Tower told me to stop. I complied. The controller told me I turned the wrong direction. I asked to return taxi entry area to turn around. He affirmed and I quickly exited the runway. Moments later I was re-cleared for take-off. [MISTAKE 4: My pre take-off cross check includes checking the heading bug - but it's not until I'm aligned with the runway. It would be wise to confirm the turn in the direction of the heading bug before entering the runway.]There were a couple of factors at play: Pilot error. I made the mistake and I own it. Tower and Ground did their jobs correctly and professionally. Construction made for a slightly more tricky runway entrance. I should have slowed down and asked questions if I wasn't 100% clear in my own mind. I was flying Aircraft X across the country VFR. I had completed a 4 hour trip from ZZZ earlier in the day and taken a couple hours off between flights to eat and prepare. This was day two of my trip and is my first cross country at this distance. This is a reminder to acknowledge the fatigue associated with long distances; and slowing down to focus on anticipated taxi/takeoff plans. Especially at airports that have construction. Key Takeaway: Spend more time during planning with the taxi-ways and expected runway departure. Have a clear mental model and; when possible; a visual model of where I need to get to and the directionof takeoff. Cross check heading bugs. Don't move until I've confirmed the runway holding sign - even at seemingly simple 1-runway airports. When lacking controlled understanding; ask the controller for clarification or time; rather than going along with them.