My storage garage has no power. I want to run a drill and a trouble light on occaision. O'reillys has some jap inverters,one plugs into cigar lighter & 2 hand held units that look like jump starters & I am told harbor freight has some(maybe that could be wired in the eng compartment. One guy talked about a deep cycle battery he uses in his storage shed w a harbor freight one & recharges it when it goes down. I am new on this, Do you guys have any suggestions on what would be the best way to go here? Thank you for your time.

An inverter has to be selected to meet the starting current requirements of the load.
I would get the 2000 W inverter from Harbour Freight currently on sale for less than $200. It should run an angle grinder until the batts go dead in a very few minutes. It aint no generator but will run basic tools and lights to make the area electric. Most boats use them in place of generaters because they are quiet, They use the main engines to recharge the battery bank.
Full load drain can be very high. I would use 2 ea group 27 batts from Walmart, in parallel. They will have a 3 year replacement warantee that no commercial 31 4d or 8d will have. The batteries will never last 3 years running the inverter but they will be replaced.
Use jumper cables from your vehicle to recharge batts, so place them for easy access.
The no-load drain is not very high but it should be turned off unless you are using it.
More expensive inverters are probably made in the same factory in Red China so why pay extra to get a black and decker or some other brand name???

I found a 2000W inverter from HDC Homier $66 on sale at one of the traveling tool shows for $44. I just run it directly off the car battery with the giant supplied alligator clips. It has a lot of automatic low and high voltage, overcurrent protection, has a fan too. A cheapie but it works fine.