So if I did just an MD, what are my options?
Many options
Can I do research between/after med school and my residency?
You can take a research year during med school. Not that uncommon to just do 5 yrs these days.
During residency - you can depending on the specialty and how the program is structured.
Can straight MDs still get matched to research residency/fellowship programs?
If you're talking about something like a PSTP (physician scientist training program) residency, then it's possible you would just need to demonstrate that you've had extensive research experience. These are extremely competitive programs and can have a lot of strings attached. Search 'pstp' on SDN and read what people way further down the path have to say. IMO, you could just do residency + fellowship + optional postdoc (depending if you have enough data, publications, etc to actually start a lab)
Can you do research during medical school?
Yes, plenty do
Would I be able to get my own research lab at a research or university hospital with just an MD?
Yes but depending on the scope of your research, pressure from your department chair, etc - it may not be easy to do.
would I need a masters?
Not really
Or is MD/PhD the only option to be seriously involved in both (basic/translational) research and medicine?
It's not the only option but it is a 'streamlined' option that gives one protected research time to develop their skill set. The further down the path you go (e.g. after residency or fellowship) the harder it will be to secure enough time to buildup your toolbox (not impossible but increasingly difficult). Also you'll have to resolve that doing the dual degree means you may not be as good as the folks who have time to master one craft. But being driven, choosing a smart problem to tackle, and a bit of luck can always help.
Overall, these are just my opinions from talking to the folks in my program, hospital system, friends further down the path, family. Take it wait ha grain of salt and good luck.