Congratulations on your first solo!
The advice given so far has merit but doesn't go far enough. A good landing starts with a stablized approach. Airspeed control and attitude (the plane's, not yours) are crucial elements for consistently good approaches and accurate and smooth touchdowns. Know what 1.3VSO is for your aircraft and practice maintaining that speed during your approach. Have in mind, every aspect of the approach path and intended touch down point when still on the downwind leg.
Discuss 1.3 VSO with your instructor. If your instructor is not familiar with the meaning and importance of VSO, and determining what it is for your aircraft, consider finding one that is.
During a power on approach, your airspeed control is pitch and altitude or sink rate control is power. Have your approach stabilized at least at 500' above the runway elevation. As you cross the runway threshhold. maintain a slightly nose high attitude with increasing back pressure on the yoke aas you ease off the power. The aircraft will pactically land itself.
Making a power off approach, use the flaps to control your rate of descent and pitch remains your airspeed control. 1.3 VSO will vary with your flap settings.
On every landing, don't just aim for the runway in general. On final, stay exactly centered and aim for your touchdown point.
As for anxiety, the more accurate and stabilized your approach, the more confidence you'll feel when crossing the fence.
On with a slight thump is safer than going for a grease job. You can practice the squeakers once you have the basics mastered.