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The Basics

2997-27 M18 18-Volt Lithium-Ion Brushless Cordless Combo Kit (7-Tool) W/ (2) 5.0 Ah Batteries, (1) Charger, (2) Tool Bags
A solid set of power tools will last you years, and Black Friday or summer holiday sales can take the sting out of the initial cost. I really like these Milwaukee Fuel brushless tools. Most of them are high quality, the batteries last well, and the waranty and support are solid. You typically end up with a tool or two with limited use in these kits, but it's often much cheaper to buy a larger kit than acquire specific tools peacemeal. Key tools you'll want from the start are a drill, impact driver, and circular saw. If you're doing to do things like build decks or remodel, add a sawzall, angle grinder, and perhaps an impact driver.
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Milwaukee 2505-22 M12 Fuel Installation Drill/Driver Kit, Compact, Forward/Reverse Switch, Keyless Chuck, LED Light, Variable Speed
The M12 series of tools from Milwaukee are great, and this Installation Driver is a good example. It's great for everything from cabinets to decks where you need to get into awkward spaces.
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Milwaukee 2401-20 M12 12-Volt Lithium-Ion Cordless 1/4 in. Hex Screwdriver (Tool-Only)
Another M12 standout is this little drill/driver. I have a couple of these scattered around the house for light drilling and screwing/unscrewing.
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Milwaukee 48-59-1808 M12 and M18 12 Volt/18 Volt Lithium-Ion Multi-Volatge Rapid Battery Charger (Non-Retail Packaging)
If you end up with both M18 and M12 tools, this combo charger takes less space and charges the big batteries quickly.
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Milwaukee Electric Tools 2365-20 M18 Rover Mounting Flood Light
A few lights are key. Battery lights aren't quite as bright, but make up for that by eliminating extension cords.
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Milwaukee 48-11-1852 M18 REDLITHIUM XC 5 Ah Lithium-Ion Extended Capacity Battery (2-Pack)
I like having a good 3 or more batteries for my tools. Typically, you'll be using two at the same time, like a drill and driver, or circular saw and jigsaw, with your third battery on the charger waiting for a swap out.
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Milwaukee 2724-21HD M18 120 MPH 450 CFM 18V Brushless Cordless Handheld Blower Kit with 8.0 Ah Battery, Rapid Charger
Cleanup your workspace, do a quick 'sweep' of the garage, and blast away leaves. The Milwaukee yard tools are pretty decent (I have this blower and the electric chainsaw) and make use of your existing batteries.
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Milwaukee M18 2 Gal. 18-Volt Lithium-ion Cordless Wet/Dry Vacuum (Tool-Only), 2.8 Amp Motor, Lightweight, Tool-Box Style for Effortless Transport and Storage
One last gem from the M18 family is this mini shoop vac. Surprisingly good suction, easy storage, and cordless ease make this perfect for cleaning up after small to medium projects.
Dewalt 20 Oz. One-Piece Steel Hammer
A standard claw hammer is the 'do it all' hammer, and will last you a lifetime (or two). I personally like the anti-vibration synthetic handles but get something nice and it won't let you down. You probably don't need a framing hammer unless you're doing a lot of framing, and in that case, I'd invest in a pneumatic nailer.
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Stanley FMHT74038A FatMax 25 Foot Tape Measure 2PK
Classic measuring tape. Buy the two packs and stash a tape or two in your kitchen, toolbox, and office.
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AWP Handyman Tool Apron 6 pockets and Loops for Tool Organization | Black & Gray | Fits up to 50" Waist Size
A tool belt might seem like overkill for a homeowner, but I'd argue it's even more important when you're generally working alone. By thoughtfully loading up your tool belt you'll save hours of 'where did I leave my hammer' and 'shoot, I'm on top of my 20' ladder and left my measuring tape in the gargage' situations.
Zircon StudSensor A100 Wall Scanner and Center/Edge Locating Stud Finder with WireWarning Detection
Zircon has been making stud finders for at least 30 years, and I like the models that have live wire detection so you can be appropriately cautious. Knocking on walls is reasonably effective, but doesn't provide the opportunities for stud-related puns that will endless delight your partner and children.

Advanced Tools

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BOSCH GLM165-25G 165 Ft Blaze Green-Beam Laser Distance Measure, Includes 2 AA Batteries, Belt Clip, & Pouch
Yeah, it does the same job at a $15 tape, but these are amazing when doing things like quickly measuring a room, or measuring high walls or objects. They're also great outside, since you can quickly measure longer distances for things like hanging lights or fencing.
BOSCH GLL3-330CG 200 Ft 12V Max Connected 360 Degree Green-Beam Laser, Includes 2.0 Ah 12V Max Lithium-Ion Battery & Charger, AA1 Alkaline Battery Adapter, Hard Carrying Case, & Accessories
More lasers! Another seemingly luxe item, until you do a complex tile project, need to align a half dozen cans or shop lights on the ceiling, or a dozen other tasks. Basically lets you project perfectly straight, level lines anywhere you need them.
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Metabo HPT Coil Framing Nailer | Pneumatic, 1-3/4-Inch up to 3-1/2-Inch | Wire Collated Coil Framing Nails | Tool-less Depth Adjustment | 5-Year Warranty | NV90AG(S)
If you're doing to be doing any framing, even just framing up a bathroom, an air nailer is a must. I like this coil nailer since you can do framining nails as well as siding.
BOSCH CM10GD Compact Miter Saw - 15 Amp Corded 10 Inch Dual-Bevel Sliding Glide Miter Saw with 60-Tooth Carbide Saw Blade
A miter saw is probably my most used power saw. My Bosch has been crusing along for a dozen years and never let me down.
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DEWALT Miter Saw Stand With Wheels (DWX726), Yellow
I avoided buying a miter saw stand for too long, and it was a dumb move. This stand folds quickly, and gets your saw out of storage and functional in a couple minutes vs. setting up on the ground or an awkward saw horse setup.
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DEWALT (DWE7491RS) 10-Inch Table Saw, 32-1/2-Inch Rip Capacity, Yellow/Black/Silver
Similar to the above, this saw stores nicely in a corner of the garage, and deploys where you need it in minutes without having to work on the ground or mess around with awkward tables.