You will meet a lot of terminology in quotes. Most of it does not change your decision. Here is what the words mean and which ones matter.
What is actually sold now
Monocrystalline silicon is essentially the whole domestic market. Made from a single silicon crystal structure, higher efficiency than the alternatives, and prices have fallen far enough that there is little reason to fit anything else.
Polycrystalline panels, made from multiple crystal fragments and recognisable by their blue mottled appearance, were common when a lot of solar content was written. They are cheaper per panel and less efficient. They have largely disappeared from the UK domestic market.
Thin film is used in some commercial and specialist applications. It has lower efficiency per square metre, which makes it a poor fit for small British roofs. Not something a domestic buyer will normally be offered.
If a quote offers you polycrystalline panels today, ask why.
The cell technologies you will see named
Within monocrystalline, manufacturers use different cell designs.
PERC was the mainstream design for years. Reliable, well understood, being superseded.
TOPCon is now the common choice in the UK domestic market. Better efficiency than PERC and better behaviour at higher temperatures.
Back contact, sometimes called ABC or IBC, moves the electrical contacts to the back of the cell. No contact lines on the front, so slightly more of the cell collects light, and it generally copes better with partial shading. It costs more.
That last point is worth more in the UK than in most markets, because British roofs are small, often overlooked by chimneys and dormers, and partial shading is normal rather than exceptional. If your roof has shading, a back-contact panel is one of the things worth asking about, alongside optimisers or microinverters.
Efficiency, and when it matters
Panel efficiency is how much of the light hitting the panel becomes electricity. Current domestic panels sit somewhere around 20% to 24%.
Efficiency only matters if roof space is your constraint. A more efficient panel gives you more watts per square metre. If you have plenty of roof, a slightly less efficient panel at a lower price per watt is usually the better buy. If your roof is small, paying for efficiency buys you a bigger system in the same area.
Work out which situation you are in before letting anyone sell you on efficiency.
Other specifications on the datasheet
Temperature coefficient How much output falls as the panel heats up. Less of an issue in Britain than in hot countries, but a lower figure is better.
Bifacial Collects light on both faces. Needs light reflected from behind, which a pitched roof does not provide. Largely irrelevant for a domestic roof installation.
Degradation rate How much output is lost each year. See panel degradation.
All-black panels An aesthetic choice. They cost a little more and produce marginally less because they run hotter. Perfectly reasonable if the appearance matters to you.
What to take from this
For most UK homes: a current monocrystalline panel from a manufacturer with a real UK presence, at a sensible price per watt, sized to fill the usable roof.
The technology choice becomes genuinely interesting in two cases: when your roof is small enough that efficiency buys you capacity, and when you have shading, where back contact and panel-level electronics both help.