Start with bottle cap openers and corkscrews, and have a couple around - you don't want the party to stop because you and your lovely spouse have a habit of leaving things in different places. Corkscrews are personal, I like the rabbit type that also spits out the cork - purists like the standard waiter's corkscrew, I say use what is comfortable for you.
Shakers. You want to mix some fun cocktails in shakers to look like a pro behind the bar. Or to show of just how jiggly the undersides of your arms have gotten over the years. Hell, maybe using the shaker more often will help with that. You can go with a standard martini shaker, or a Boston shaker, which has the sturdy mixing glass and the metal cup and you can press them both together to shake your concoction. Either way can be slightly messy, make sure towels are also on your bar tools list.
Measuring - you want some two-ounce glass measures, pyrex has good ones but you can likely get some at the dollar store. Make sure they are well marked. A set of measuring spoons is also handy.
And speaking of spoons, one of those long-handled bar spoons is quite effective for mixing in a tall glass or pitcher.
Which leads us to pitchers. A couple of sizes, clear if possible, so that you can see what you are doing. They are perfect for making larger quantities of cocktails and mixed drinks. You know, in case you have guests. Or it has been a really bad day. Or you suffer from thirst.
Ice bucket, with lid please. And tongs, we are not animals. Optional: wine or champagne bucket. But I find the bar fridge is fine for keeping the wine cool.
Bar strainer, to keep things like ice cubes and fruit from plopping into your drink and causing a splash. Unless, of course, you like that sort of thing. In that case, increase the order for bar mops.
Lint free towels - for polishing glassware. Use the terry types for mopping up. And trust me, you will need a few. Things get slippery as the night wears on. Through no fault of my own of course...
Decanter, for letting your wine breathe, heavily. If you hear it start to pant - it's ready.
Blender, for blended drinks. Kinda obvious, that one. Don't use the one from your kitchen, you don't want your frosty margarita tasting like last night's salsa tonnato.
Muddler, for crushing herbs or fruit in your cocktail. Or for vanquishing your enemies. Your choice.
Ice crusher. Manual or electric.
It's the little things...
Citrus reamer, zester, straws, trays, picks, stir sticks, cutting boards and paring knives. Also a couple of bartender's recipe and reference books are quite good to have around.
And of course, it is handy to have a sink nearby for quick washing up.
Let me know when you have all those items assembled. Then we will move on to Stocking the Bar: Entertainment!