The upper Spokane is handy to you, and is a pretty good first float. It offering a variety: a couple of small but not insignificant roller waves, some riffles, some shallow bars and deeper rocks, a usual upstream wind, some really nice frogwater for basking and having a beer on a nice afternoon, The best float is to put in at Corbin Park in Post Falls, and float down to Harvard Rd. bridge in Liberty Lake. The takeouts below there are not for first-timers. At Harvard Rd. the takeout is river right just after the bridge, and rowing a raft from the preferred channel to the takeout requires some gumption. So basically you're likely to get a bit of everything, just not too much of anything. It gets pretty low after they close in the Dam around the 4th of July.
Of course the river in WA is closed to fishing now. And while the flows in this stretch today are pretty favorable, it's colder than you'd want if you got wet. You're on the wrong side of breakup to get in a hurry. FYI The best gage to use for flows in this stretch is the one at Post Falls Dam,
https://waterdata.usgs.gov/monitoring-location/12419000/. The river loses flow to the aquifer all through this stretch. I like this stretch 2000-6000 cfs. June's pretty ideal for a lotta reasons so it may fit your schedule.
The North Fork of the Cd'A is also a short trip away, and offers an early and not particulary intense breakup period, as well as dandy fishing. It's still winter up there. Best gage:
https://waterdata.usgs.gov/id/nwis/dv/?site_no=12413000, and the most knowledgable guy I know on this in terms of flows year around is Bo at Silver Bow.
I guess I'd recommend spending less time driving and more time floating your first few trips.
As to spare oars, get one the same length. Otherwise, a used one is good, and use anything before you decide. I think 7 1/2 foot oars on your boat is pretty short...you may want extensions.
A pfd for you and your companion, a drybag full of spares (an oar lock, other boat related stuff), safety items (small first aid kit, whistle, etc.), a throwbag or two and some line and you're on the river, bro.