Budget for the grinder before you choose the machine
This is the one that costs people money. A machine without a built-in grinder is not finished, and pairing it with a blade grinder will make an excellent machine produce undrinkable espresso, because a blade grinder produces a mix of dust and boulders rather than a consistent particle size. If your total budget is fixed, a machine with a decent grinder built in will beat a better machine plus whatever grinder you can still afford. That single fact reshuffles most beginner shortlists.
Heat-up time is a feature you will use every day
A machine that needs twenty minutes to be stable is a machine you will use at weekends. A thermojet or thermoblock system that is ready in seconds changes espresso from an occasion into a habit, and habit is what makes you good at it. Look at the heat-up figure on the spec sheet before you look at the boiler count.
Automatic milk is either the whole point or a waste
Be honest about which drink you actually make. If it is a flat white every morning, an automatic wand or a carafe system earns its place and removes the skill you would otherwise spend two months acquiring. If you drink espresso black, milk automation is money spent on a feature you will use twice, and that budget belongs in the grinder or in the machine's temperature stability.
Pressurised baskets: helpful at first, a ceiling later
Many beginner machines ship with a pressurised (dual-wall) basket, which fakes crema by forcing coffee through a single small hole. It makes bad grinding produce acceptable results, which is genuinely useful in week one. It also means you are not tasting what the machine can do. Check that the machine can take a standard non-pressurised basket too, so the training wheels come off when you are ready.
Buy for the counter you have
Measure before you order, including the height with the water tank lid open if the machine lives under a wall cabinet, and the depth, which is where super-automatics surprise people. A machine that does not fit gets used somewhere inconvenient, and a machine that is inconvenient stops getting used.