In PostGIS, for points with latitude and longitude there is geography datatype.
To add a column:
alter table your_table add column geog geography;
To insert data:
insert into your_table (geog) values ('SRID=4326;POINT(longitude latitude)');
4326 is Spatial Reference ID that says it's data in degrees longitude and latitude, same as in GPS. More about it: http://epsg.io/4326
Order is Longitude, Latitude - so if you plot it as the map, it is (x, y).
To find closest point you need first to create spatial index:
create index on your_table using gist (geog);
and then request, say, 5 closest to a given point:
select *
from your_table
order by geog <-> 'SRID=4326;POINT(lon lat)'
limit 5;