This is what I would do.
1) Get your materials.
Since I don't know anything about your particular stand I can't tell you exactly what to use, but here are some suggestions. sand paper, tack cloth, Wood filler/putty, putty knife, paintable latex caulk, latex paint, paint brushes/rollers, masking tape, butcher paper, and rubber gloves.
2) Prepare the stand.
First you will want to mask the tank to avoid getting dust and paint on/in it. Use the masking tape and butcher paper for this. Try to leave about a 1/4" gap between the bottom of the tank and the stand. I'll explain the purpose of this later. Also make it so that you have access to be able to feed, because this will take several days to finish. Now fill any cracks, screw holes, nail holes, gouges, etc. with the wood filler. You may have to sand and re-apply the filler depending on the product so just follow the instructions on the filler container. Once the filler has cured, sand the entire stand to remove any irregularities that you don't want to see under the paint.
3) Since you are not planning on removing the tank from the stand anytime soon, the next thing I would do is seal the tank to the stand.
This should make a barier so that water won't get under the tank and cause mold, mildew, and eventually rot the wood. To do this I would lay a bead of the paintable caulk all the way around the perimeter of the tank where it contacts the stand. Let it overlap the masking tape and cover the 1/4" gap that you left in step 2. Now smooth it out with a gloved finger and let it FULLY cure per the instructions on the tube.
4) Now apply the paint.
It will probably take several coats so be patient and don't put it on to thick. Depending on the size of the sides to be painted, I would use a fine nap roller everywhere I could. It should make a much more even coat than a brush, but there are some areas that will have to be done with a brush. Let each coat dry before applying the next. It would also be a good idea to sand lightly between coats with a 200 grit or finer sand paper, but it is not completely necessary to do so. If you choose to sand between coats remember to use the tack cloth to remove all the dust before applying the next coat.
5) Seal the paint.
Once you are satisfied with the paint you need to seal the stand to prevent any moisture getting into the wood. Apply the polyeurathane per the manufacturers instructions being careful to evenly coat the ENTIRE stand. You should probably do 2-3 coats of the poly. This step is necessary to make a waterproof finish. Sometimes water can get under the paint and cause a blister looking thing and you don't want that.
6) Remove the masking material and enjoy your hard work.
If you ever decide to move the tank it would be a good idea to remove it from the stand. If you do it would be a good time to finish the top. I would start that by removing all of the caulk and sanding the top and feathering the edges that are painted with the raw wood. then follow the procedure above and you should never be able to tell that the top was finished separately.
This is a general idea of how to finish a piece of woodwork, but it is not exhaustive and other people might know of a better way of doing it. I hope it helps.
