The truth is almost all ir guns are not very accurate. The vast magority are up to 1ºC (basically 2ºF) in error. The ebay ones you have posted have incomplete specs listed I would NEVER buy anything unless I had complete specs in writting. The third one is unacceptable (IMO) up 4ºF in error is simply too far. That said many, many here feel this is completely ok. (accurite and hydrofarms share this spec)

What I would look for is the D:S ratio and battery type. For Royals a D:S of 1:1, 2:1, 6:1 are best beyond this it is difficult to stay in the 'sweet spot' for optical focus. (1:1 is inside 4 inches and 6:1 12-24 inches 80-1 for example is 60-80 inches) I would suggest a common battery type A, AA, AAA 9v ect. My first gun uses 2cr3 it also has a hard switch 30 dollars if you forget to turn it off. Something to avoid.