First let me say: I have been running direct for years with IEMs and no amp. There are a lot of good choices. I will share my exprience.
How you run direct and get good results - with no amp - in a church setting unfortunately in controlled by the sound person. Our "sound person" is the pastor's 25 year old daughter who is a volunteer and really knows nothing about sound, nor is she a musician of any type. This seems to be the norm in church situations, volunteers with no clue about running sound.
So, for me, every time I have ever tried to use any type of DI with EQ, etc. on it, my sound always ends up coming through distorted or "invisible". Always sounds great in the IEMs, but not in the house. So all I run at church is my bass into a Mark Bass Compressore into a Radial JDI. She says she "likes that bass because it doesn't rattle the speakers".
So for most church settings, I say the simpler, the better. Passive DI with an actice bass, Active Di with a passive bass.
So I have tried almost every reccomendation above, and I ended up using a Radial JDI, Radial J48, and a BBE DI100X (or is it D1000X?) - the active one with the BBE processor built in. The ones with all the extra knobs just cause problems for amateur sound people.