First, I am going to assume you mean an analog (or mostly analog) console. If I missed something please disregard the rest!
There is "character" and there is noise and distortion. To some they are one and the same, and that's not a judgement, if it works for you it works.
Personally, I would shy away from the lower end of the spectrum, including Mackie, A&H, Yamaha, and Soundcraft. All of these lines have been "value engineered" to get the prices down, and the first victim of value engineering is the power supply. Designing (and building) a good power supply is not cheap. You would think otherwise, I mean there isn't anything new in linear supplies, and very little new (applicable to us anyway) in switching supplies.
Where it will cause you grief is headroom and transient response. If you are really careful you can work around it, but the whole idea of a physical mixer is that you don't have to be constantly worrying about levels, analog is supposed to be more forgiving then digital. But in an inexpensive mixer you have to be every bit as careful, which would kill the vibe!
Speck builds brilliant stuff! His mixers are darned near transparent - which may not be what you are looking for, his equalizers are amazingly musical, and straddle the line between character and neutral. I think the only mixer he still sells is the LiLo, which is a line level only mixer that you probably can't clip. They were around $10k for a 16x2 when they were released. That was a little too rich for my bank account.
If you are looking for character over convenience look for an older (more experienced?) mixer from Ramsa, Yamaha, A&H, or Soundcraft. The problem you may run into is that most of them will be fairly large, with high channel counts - that's what folks wanted. Crest and Tangent made smaller mixers designed for live sound reinforcement, and may have fewer features you won't be using anyway.
There is always Altec and RCA - lots of character, but lots of maintenance as well, since they are very old at this point.
Someone above mentioned using a summing box. That won't address the hand's on aspect, but it can provide character. Look for a passive summer and an active makeup gain stage, then choose the gain stage to suit your tastes.