Hi Allison, thanks for your question. I love Rex Begonias!  They are great house plants.  Be careful though, they can be addictive as they come in so many beautiful color combinations.  When I lived in Texas I had a collection of about 30 of these plants and would have never thought that they were considered fussy to grow.  After reading up on these plants from various sources I would give you these tips.  First start with a fast draining potting mix.  This can include those with additions such as pumice, or perlite.  If the potting mix you choose does not have these additions it is possible to purchase these additions separately and ad some to the mix before you pot.  The Begonia Society recommends a soilless mix for these houseplants.  I am sure that any garden center you visit will be able to advise you on which mix should be good for your plants. Local places such as Schmidt’s, Shonnard’s, Homegrown, and Garlands or even Bi Mart and Home Depot sell such potting mixes.  When potting up small plants such as those you have purchased be sure to put them in a small pot not all that much bigger than their root balls. Allow maybe an inch to an inch and a half all the way around the root ball.  I found one source that recommended not repotting these guys very often (once every 2 or 3 years) and another that said to repot yearly.  I used to repot mine every year or so depending on how fast they were growing and the condition of the potting mix.  The location in your home is critical.  Avoid placing them near a heat register as they will dry out too quickly.  They prefer temperatures around 70 and are not happy below 60 degrees.  Since your apartment faces north a plant light is definitely something that you will want to use.  These plants will want as much INDIRECT bright light as you can provide for them. Don’t push them right up under your grow light, it can bleach out the leaves.  Use your grow light at least 8 hours a day.  The other thing I highly recommend is the gravel tray you mentioned.  Be sure that the bottom of the plants never stand in water.  While begonias prefer humidity of around 50% they do not tolerate wet feet.  Keep the roots well above the water level.  You can do this by using a saucer under you plant and set it on top the gravel.  Watch the leaf margins of your plants, any browning indicates that the humidity is not optimal.  A humidifier can also help.  Most begonias are killed due to overwatering.  Allow the potting mix to become dry in between watering.  Do not allow the plants to wilt.  Water the plants over the sink, allow the water to drain through the pot; when it quits draining place them back into their saucer.  If water collects in the saucer, empty it.  To combat powdery mildew be sure to keep air circulating around the plants, do not crowd them too close together.  I would not put them into bell jar because of this.  When these plants are happy they do bloom, nothing really showy but at least it is an indicator that all is well with them. Be sure to remove any dead leaves and keep an eye out for any insect or disease problems.  Most importantly have fun!  Houseplants are a great hobby and a much needed gardening fix over the winter.