Buy them as you need them if you are on a limited budget. This way you buy what you need, and don't have to "think" you will need it.

-Tape measures at least 3.
-Scissors at least 2.
-Pipe wrenches at least 2. (I like the blue handled quick-adjust ones. They fit most residential pipes, and then get 1 or 2 large ones when you need them.) Good yard sale item to find.
-Tape. Masking, Duct, Electrical. At least 1 of each.
-Screwdriver. Pick up a complete 'set' of craftsmen pro. They cost a little more than standard but the grip is much better especially in the rain.
-Hammers get at least 2 or 3 depending on what you plan to do/type and size.
-Nail pullers. 2 or 3 depending how hard nails you want are to get. THe flat/drywall kind and also the kind you mash with a hammer for removing from decks/etc.
-Cheap multi-LED flashlight to keep in tool kit as utility light.
-Headlamp
-6' or 8' ladder and a 10'+ if you have the need.
-Pen/Pencil
-Drill + Drill bits and misc phillips/square/hex
-Wash buckets or 5g buckets
-Broom
-2-3 crescent wrenches in varying sizes (small->large)
-Needle Nose & Standard Pliers. (I like Knipex high voltage rated)
-Couple pocket knives
-Box Cutter/Razor blade knife
-2 Shovels, Pick Axe
-IF in snow, snow shovel

I like Milwaukee lithium ion batteries/tools. I have almost the complete v28 set and use the tools for everything! For impact driver I don't think you can beat the Hilti 14.4 it's light, the lights are bright, and the batteries literally last longer than any other battery tool I've used!

Depending on your property you may need some pruning tools too.
A wheel barrow, a wagon, a rake, a sawzall, etc.