There are a lot of options for a briefcase-style pedal case. I prefer the hard cases because you can bolt everything down including an AC power supply and it's neat and effective. Definitely recommend the power supply. Dunlop DC brick is a good one, but you can use almost any supply with a splitter.
Stuff I recommend:
Overdrive. For flexibility, the 5:50 (and F50) are probably best set for low-ish gain (AC/DC style) and coupled with an overdrive. I use both the OD808 and BB Preamp. They are very nice, and also different from each other. There are a million varieties. I recommend that you pick a good one early, rather than playing with 20 different $39 version before finding the light.
I set up my tone like this:
Clean: Very clean
Clean + Overdrive: a bit of dirt, bluesy drive
Gain: Moderate Distortion
Gain + Overdrive: Heavier Rhythm and Clear Leads
Gain + Contour + Overdrive: Over the top rhythm, singing leads
That's a lot of flexibility for an amp and one pedal.
After that, I find a phaser (MXR EVH phase 90) and delay (almost any will do) awfully nice to have.
For vintage delay (tape loop style) the Time Factor, El Capistan and Flashback are good choices. The FB is cheapest and smallest. I have used a Boss DD-3 for decades, and that's a good cheap serviceable delay, but these days there is so much more available.
I also use a boost for leads. I have both an MXR micro amp and a BB EP booster for this. Both are great.
You'll want a tuner. I have used a TU-2 for years and recently got a TC Polytune. Both are great.
Then a good wah is indispensable.
A volume pedal could be used in place of a volume boost pedal, and also for volume swells, but I have found that if I'm pressed for space it's the first pedal I discard.
I highly recommend using the amp's FX loop. I typically run:
In front of amp:
Tuner
Wah
Phaser
Flanger
Overdrive
Distortion
In loop:
EQ (can be used as a boost, too)
Chorus
Delay
Boost
I also like to have my amp switch in the case as well.
Once it gets out of hand, you should look at the Pedaltrain cases. They are REALLY nice. I'm running a PT Pro, but it's way out of hand. The smaller ones have optional hard briefcases that are reasonably nice.
My briefcase and what it turned into: