1. For seedlings, a T-5 would be ideal.

2. One of the biggest problems indoor growers face is too much light. If the plants get to much light they begin to shrink, pale, thin, droop, and roll their lights in an effort to escape from it. This is a problem you don't want! Remember, keeping the light a little too far away is never a problem. That's why outdoor plants never get too much light. Allow your plants to grow into their space. About 2-3 ft from the plants canopy will do and as the plants grow you should adjust the height accordingly.

3. Your seedlings can tolerate 24 hrs of light but once they get into the veg stage you'll need to cut that down to 18 hrs on-6 hrs off using a timer. Your plants should be safe and sound while you are gone

4. T-5 fixtures have the ballast and reflector built into it. There are also lights stands you could use to hang your lights from. I have a provided a link below with good options to choose from.

5. You want all of your plants to get some light but if some need more light than others it's OK to place your plants accordingly.

If you have any more questions let me know, I would be glad to help!

Here is a link that might be useful: Groflo Hydroponics Fluorescent Lighting

Can tropical house plants, such as a small TI, Coleus and Begonia, do ok indoors for the winter using spiral fluorescent bulbs? Example: "Sunlite" brand, 900 lumens, 13 watts (60 watt equivalent), warm white color 2700 Kelvin.
Any suggestions will be so appreciated.
Thanks!

It would be better than nothing. But Coleus and Begonia, at least, are low light plants. They still need more than 900 lumens. Over 10,000 lumens and they'd still probably be a bit short.

Put them in a sunny southern window if possible and supplement with as much light as you can.