Firstly, the quality of advice regarding coffee on this forum is probably as poor as the advice you would get on a coffee forum if you asked there about mountain biking.
Try coffeegeek.com or homebarista.com for useful information and advice.
In my experience, fwiw, I started with a stovetop and got fair coffee with off the shelf, pre-ground Illy. Slightly bitter though. I then purchased a Gaggia Evolution (similar internals to the Classic) better espresso, but inconsistent (mainly due to temperature variation and pre-ground coffee deteriorating rapidly after opening, and lack of control over extraction times. Got a burr grinder large improvement with fresh coffee, but a noticeable deterioration after two weeks from roasting
Purchased a coffee roaster and now only roast enough for a couple of weeks. From day of roasting there is an improvement in espresso for 2-3 days, good espresso for the next week or two, then a noticeable drop after two weeks.
I was still struggling with inconsistent temperature, so got a Heatexchanger machine and now get Espresso I’m very happy with.
Every step in this progression has improved flavour and/or crema in my espresso.
I would echo the Aeropress can produce very good coffee, (but not espresso!)
To sum up for fine espresso you need: consistent and accurate temperature control, 92-93 degree centigrade. Fresh coffee, less than two weeks from roasting. Ground within a few minutes of using. Good quality beans. Anything else, in my experience will not produce fine espresso. Cafitiere, filter machines and vac-pots are slightly less fussy, but not massively so.
Nesspresso’s contribution to coffee is the same as Argos’s contribution to downhill racing. IMHO.