Always measure pre boil gravity. You should know what to expect when you plan your recipe. Then when you have the pre boil gravity you can make a course correction to get your your intended original gravity.
Beer Alchemy shows it like this on my brew day instructions sheet:
Gravity Before Boil: 1.060 SG (15.3 Brix)
Original Gravity: 1.070 SG (17.7 Brix)
Final Gravity: 1.014 SG (9.4 Brix)
Volume Before Boil: 13.50 US gals
Volume After Boil: 12.50 US gals
Volume Transferred: 10.50 US gals
Water Added To Dilute: 0.0 qts
Volume At Pitching: 10.50 US gals
Volume Of Finished Beer: 10.00 US gals
Total Water Required: 16.77 US gals
Total Grain: 27lb 4oz
These are all expected values
If I hit my volume right (and I fly sparge so that is a given if I don't get distracted and over collect) and Gravity Before Boil is low I know I undershot expected efficiency. I then have a variety of ways to get to planned OG. Usually what I would do is collect another 0.5 or 1 gallon and then boil longer. I'd start my 60 minute timer when kettle volume reached the original planned 13.5 gallons. To boil 14.5 gallons in a 15.5 gallon pot calls for fermcap but works out fine. Other options would be to boil longer/harder without sparging extra. I could check an evaporation calculator and see what volume I need to get to hit the intended pre boil gravity.
As for how to do it I use a refractometer for pre boil gravity. That is easy and the cheap ones seem to work quite well. It is nice that Beer Alchemy shows me expected gravity in SG and Brix units since refactometer reads brix.
If using hydrometer the ice bath methods described above are fine. If collecting a hydrometer sample I'd add the sample back into the boil kettle during the boil. No point in dumping it unless you are like @Stillraining and want to keep full hydrometer bottles standing around during brew day. Accident waiting to happen I think
I do get a hydrometer sample for original gravity using the chilled wort. I collect this during transfer to the fermentors. I can actually get what I need from my pump lines. I don't add the post boil post chill wort back to the fermentors. That is a pre ferment sample to taste.