You won't get a clean sound out of an amplifier if the signal you are sending into it is high enough to push it into clipping, or if the gain the amp is set to is high enough to push it into clipping.
So for a clean sound you need to be using an amplifier that has a lot of headroom before it clips and make sure you aren't sending it such a hot signal that you use up all the clean headroom. The pickups are a factor, but the instrument's volume control, how hard you pick and amp and effects settings make more of a difference. You can play distorted heavy metal on a low-output Stratocaster and clean jazz on a high-output ESP. Lapsteels tend to have quite high output pickpups, at least my two do. This is because the strings are usually a long way above the pickup so it needs to have more output to compensate, and also to give a usable output level as the string vibrations get less to add more sustain
For a clean sound you could try this.
For the amp pick a Fender, preferably Blackface. Try a Princeton or a Twin Reverb. In e.g. Amplitube pay close attention to the plugin input gain. Keep it out of the red. Keep the amp model volume and tone controls fairly low, especially the volume. That will give a clean sound, but one probably lacking in sustain. A mildly cranked Twin or similar might get you a clean enough sound with enough sustain on it's own if you get the settings exactly right.
Otherwise, to get the sustain back add a compressor in front of the amp (between steel and amp). Either something like a Dynacomp pedal or a full-blown VST one. Keep the attack short, release can be fairly long. You need it to be adding a few dB as the signal from the steel starts to drop off. Watch how much gain it adds, too much will overdrive the amp.
Then add spring reverb.
Or get a small valve combo, run it at a low gain and volume setting where it's clean and put a microphone in front of it. Add a pedal compressor if needed and there you go. Can be far easier than trying to get the same result out of software.
Quite a lot of clean country recorded pedal steel is done by plugging the steel into the desk, no amp, then compressing and eqing it. Or mixing a direct signal with one from an amp. Might be worth a try as well.
Edited to add - presets aren't really much use in this kind of situation, unless the preset was created using the same instrument as you, the same instrument settings as you, played in the way you play by someone with the same touch as you and the oreset was created by someone aware of and aiming for the sound in your head. :-)