The most relevant information is just off the bottom left-hand corner of your picture: how is the power supply rated? How much power can it provide on the 3.3V and 5V lines that the AGP slot gets most of its power from?
That said, this is a P3 system, there's no point in going for one of the final AGP cards like the Radeon 9700Pro that pushed power supplies to their limits.
That "green bracket" in the AGP slot is what Intel calls a "Graphics Performance Accelerator" or "GPA", in other words 4MB of SDRAM for the integrated graphics controller in the i815 GMCH (northbridge - that square black chip just to the right of the CPU and RAM. Without the GPA, the performance of the integrated graphics is - even by 2000 standards - abysmal. With the GPA the performance increases to very bad. But if you want to use your own AGP card, that's all pretty irrelevant. Choose a suitable card, pull the GPA out and insert the card.
The 815 chipset has a universal AGP 4x slot, so will accept any AGP card (the 8X cards will run at 4X and 1.5V, but as mentioned above, those late 8X AGP cards are utter overkill for a P3 system like this anyway, so running at 4X AGP spec won't matter in the slightest, the CPU will be bottlenecking anyway). As for which card - take your pick. Win98SE supports pretty much anything out there on AGP, so I'd suggest finding something period-correct. If you want to go nVida, that would be a late TNT2 or early GeForce, ATi would be a late Rage128 or early Radeon - or you could try something more exotic like an S3 Savage2000 or a Matrox G450. Or of course a Voodoo4 or 5 if you want to splurge idiotically. What would be best depende entirely on what you intend to do with it all. The G450 has by far the best RAMDAC and analog filters, so will give you the sharpest, crispest VGA picture at higher resolutions, and the GeForce and Radeon offer the best gaming performance.
As for drivers, you need chipset drivers for the i815, and probably also audio drivers (some or other AC'97 codec). Both HP (who took over Compaq) and Intel still have drivers for this kind of stuff online. I downloaded the Win98SE i815 drivers from the Intel site for a marginally newer Compaq motherboard last week. I'd recommend getting the chipset drivers there, and sound drivers wherever you can find them - which might end up being HP.
