Almost every argument about home espresso comes down to three mechanical questions. None of them are about the brand on the front.
Espresso is brewed by forcing water through a compacted bed of coffee at pressure. For that to work, the grind has to be fine enough to build resistance and — far more importantly — even enough that the water cannot find an easy path through. A grinder that produces a wide spread of particle sizes gives water somewhere to escape, and the shot runs fast and thin no matter how good the machine is. This is why a capable machine on a weak grinder still makes weak espresso, and why every pairing on this page includes both. As a rough allocation, a third to a half of the total budget belongs to grinding.
Burr geometry is the usual dividing line, though it is worth being honest about what it does and does not tell you. In a conical set a cone turns inside a ring and gravity helps pull the beans down through a narrowing gap. In a flat set two ring-shaped burrs face each other and the coffee is thrown outward from the centre, which takes more force and higher motor speed. Beyond that mechanical difference, the popular claim that one geometry inherently grinds more evenly than the other is genuinely contested — in practice the quality of the specific burr set matters far more than whether it is flat or conical, so treat “flat is more even” as a rule of thumb rather than a fact. Single-dosing grinders — where you weigh in exactly the coffee you are about to brew — are a separate idea again, and exist mainly to avoid stale grounds sitting in a hopper.
A single boiler machine heats one vessel and has to switch between brew temperature and steam temperature. You pull the shot, wait for it to climb, then steam. That wait is perfectly workable for one or two drinks, and it is how most people learn.
A heat exchanger passes brew water through a steam boiler, so you can brew and steam without waiting. A dual boiler keeps two separate vessels at two temperatures and does the same thing with more stability and more cost. If you make milk drinks for one person, a single boiler is fine. If you make three cappuccinos back to back on a weekday morning, the waiting is the thing that will make you resent the machine.
An all-in-one machine puts the grinder inside the body. That is genuinely less to buy, less to house, and less to learn. The trade is that the grinder is the part you would normally upgrade first, and now you cannot upgrade it without replacing the whole machine. If your counter is short and you want one appliance, that trade is worth making. If you expect to still be interested in two years, separates give you somewhere to go.
Once you own a machine, everything you add has to match its brew group. This is where money gets wasted, because the number printed on the box is not always the number you need: most 54 mm machines take a 53.3 mm tamper, not a 54 mm one, and Lelit's 57 mm format is one millimetre off the 58 mm commercial standard, which makes standard parts useless. Before buying a tamper, basket or funnel, check what your machine actually takes — the Fit Finder lists the sizes for each family with sources.