Things such as military bearing, decent APFT score and working well with others play into having a good OER.
The best advice that was ever given to me was from an O-6 who said “Don’t worry about it, if you’re doing the right thing your OER will write itself.” I live by it and it hasn’t failed me yet. I absolutely agree with @brock it is fair to ask (and you should ask!) what your rater and senior rater’s expectations are. The keys to my success have been: focus on constant self-improvement; think of every task as an opportunity to excel; and most importantly: take care of your folks (whether they be Soldiers, Civilians, Contractors, etc…) If you haven’t already, I’d highly recommend reading (and re-reading) ADP 6-22 (Army Leadership). It only contains about 9 pages of content, so it’s an easy read, but the real challenge is applying it to yourself to better understand your own strengths/weaknesses. You can pull it off of http://www.adp.army.mil

What is your advice for standing out in a positive way to your supervisors?
@logisticus hit the nail on the head. Initiative is the name of the game, so put yourself out there and don’t be afraid to make mistakes. When I first arrived to my current unit (MEDDAC), I introduced myself to the Company Commander (even though he wasn’t in my rating chain) and told him I’d be interested in any self-development opportunities he could afford me. Within two months, I was a Range OIC, Summary Courts Martial Officer, received a slot to compete for the German Armed Forces Proficiency Badge, and I met a lot of great folks along the way that I would, otherwise, have never had the chance to meet.

What are the Captains and 1LTs looking for when I first arrive at my new unit?
First impressions are everything. I can guarantee that they will look for these three things when you first arrive: 1. Timeliness: if you say you’re going to report at 0730 then plan to get there at least five or ten minutes early); 2. Appearance: make sure you and your uniform look presentable (IAW AR 670-1); 3. Humility: don’t ever think that because you’re an officer you’re superior to everyone around you (heard a story from a fellow CPT regarding one of the LTs at his first unit telling the SGM to stand at attention when he was talking to him– needless to say, it didn’t end well for that 2LT). You’re going to be the new guy so don’t think that you have to know everything “I’ll get back to you” is a perfectly acceptable answer to something you don’t know but just ensure you actually get back to that individual with the info requested. Lastly, you can expect to be on the receiving end of a lot of LT jokes but don’t take any of it personally, we’ve all been there.

What are some tips on creating a good relationship with my supervisors?
Anything that you can do to make their lives easier. In addition to accomplishing your mission, here are a few other easy victories for building a good relationship: 1. Accountability: Let your rater know when you’re going to be out of the office for appointments, meetings, etc… (Sharing your Outlook calendar is a good method for this one); 2. Training: Keep up-to-date with all of your annual training requirements. The less your name comes up on any hit list, the better.; 3. MEDPROS: Never, ever become Red on MEDPROS (i.e. Dental/Vision/Hearing/PHA).

How can I present myself as the go to 2LT without being a teachers pet?
I actually had a discussion about this last week with one of the NCO’s I was on duty with and I absolutely agree with him. His thoughts were: “Anyone who has that mentality is wrong. I was the go-to SPC in my last unit because I showed up to work early, stayed late, and took jobs nobody else wanted.” If you’re designated as the go-to LT then it’s because you worked for that, so take pride in it. Bottom line: stay hungry, stay humble.