Need Help... Long-time Hobbyist, New to Lighting

Hi,  ...am looking for help with lighting.  Have been a long-time hobbyist using a single, on-camera flash, but I am looking to expand into off-camera lighting using more than one flash/light.  I've been a hobbyist for over 20 years, but in the last 2-3 years, I've been getting asked to do some paid gigs on the side.  It really has be thinking about expanding my photog "world" into learning more about lighting.  I have a day job, and I'm not looking to go into photography as a business.  I am looking, however, to improve my photography in the area of additional lighting.  My photos are largely of family, friends, co-workers, and I often volunteer to be the photographer at events related to work, church, get-togethers with friend/family, etc.  Not likely to expand out of these types of subjects/events, but I genuinely want to improve and expand into more advanced lighting.

Below are some pics I did for my church...  using a single, on-camera flash.  I'm not happy with:

• flash reflections from eyeglasses
• flash reflections from the sheen of background pics taped up to background material
• hard, direct flash lighting in general

What can I do to improve?  Get a second flash? Get studio strobes (what kind)? umbrellas and/or soft boxes?  All the above?  Looking for any suggestions.