Hi H, Super Easy
A heat mat (if needed), tray(s) w dome (dome if needed) and a little light setup. You can build or buy complete, depends on your time and budget.
A gathered homemade setup might look like this and cost about $100.You have a tray, 72 pocket insert and dome (all 1020 sized). Heated mat with thermostat and a light with homemade PVC frame for hanging. The mat is controlled by the thermostat, the light is controlled by the timer you see on the power strip. Mat is on as thermostat requires, light runs 10 - 12 hours a day per timer.
Most general germination takes place at 65 - 75 degrees so the mat could actually be optional in a mild room or area, doemto for that matter but the dome is help in keeping to soil moist. In general you can start most garden plants like this but not all transplant as well as other. I would suggest about 4 weeks +/- 1 max is the duration plants can be grown in a tray setup like below, much longer than that and they are too big so plan accordingly. Problems at 4 weeks include roots getting to long and numerous and overhead watering can become non effective or even detrimental.
PVC, Power Strip, Timer, (if you choose this type of set up) Potting Mix and Seeds you can get locally at Home Centers. If "hydroponics" are popular you should be able to get everything else there. If not lots of places on line.
I prefer the mats with a thermostat as this allows you to set the optimal temperature, most of the non thermostat controlled say they regulate to 10 degrees above ambient temperature, on a warm day that could have negative consequences.
I also prefer non draining trays for germination, moist is best and so I try and keep the water moderate. I'll typically water lightly with a Dixie cup and then try and keep things moist with a mister. I also keeps water off the heat pad.
https://www.greenhousemegastore.com/product/fluorescent-grow-light-system/lighting
https://www.greenhousemegastore.com/category/flats-trays-inserts
https://www.greenhousemegastore.com...mp-start-grow-light-system/heat-mats-chambers
http://www.growerssupply.com/farm/supplies/cat1a;gs_seed_starting.html