Which background are we supposed to map to?

You need to realign the imagery to gps traces and Strava heatmap data before using and best way to do that is to switch off the mapped data layer or switch wireframe mode first. The satellite imagery is composed of many stitched images and the alignment will need to be readjusted as you edit in different areas. You can normally find the latest imagery by moving to known recently developed areas and comparing. What imagery you use will depend on what is available locally so you will need to decide that yourself for your locality and you might find that selecting between several different sources while editing produces the best result.
https://wiki.openstreetmap.org/wiki/Using_Imagery

To add a little bit to what nevw's already said...

If there are lots of GPS traces (either visible in from OSM or via one of the Strava layers) then that's the best thing to align to. Individual GPS traces may be a few meters out either way, but the average of lots of traces will generally be pretty good (unless you're in unusual circumstances such as under a cliff for example).

However not everywhere has lots of GPS traces, and in that case you may be able to use some elements of the OS OpenData Streetview imagery to determine "what is correct":

• The position of roads is normally pretty good, although you can't always infer the type of highway (e.g. unclassified/service/track) from it.
• The position of streams and ditches are normally pretty good, except when they're adjacent to a road, in which case the OS tends to artificially move the ditch away from the road. The OS's stream data is also quite old and where waterways have changed may be out of date. Also the "top end" of streams (bogs, springs etc.) is often a bit rubbish in the OS data.
• Buildings in the OS Streetview data are not much use for alignment. You can say "there probably was a building there" but not exactly what shape and not exactly where.

Of the other layers, I've found near me (Notts / Derbys) that the other layers vary in terms of how new they are and how offset they are. Often one layer (e.g. ESRI) is newer, and very useful for that, but offset.

In each of the different OSM editors you can adjust imagery offset so that if you find newer imagery that is definitely "in the wrong place" you can move it.