Justin,
When I did my first partial mash I wanted to try something that was difficult to accomplish with extract only, so I chose a Dry Stout. I didn't want to purchase any additional equipment but I wanted to try fly sparging rather than brew in a bag, so I used a combination of my 5 gal kettle and my bottling bucket for mashing.
Process was simple. I preheat my oven to the lowest temperature in allowed - 170. I placed a 5 gallon paint strainer bag in my brew kettle and brought mash water up to strike temperature in it on the stovetop. When at temperature, I stirred in the grain and transferred to the oven. By removing every 15 minutes to check temperature, the oven held step temperature even though it was set hotter (having an internal oven thermometer helped.)
While mashing, I heated water for sparging in a second pot. When the mash step time was complete, I placed my bottling bucket on a chair, removed the kettle from the oven and carefully transferred the paint strainer bag with grain to the bottling bucket. I placed a small colander over the grain to avoid channeling and slowly poured in the wort.
I then put the kettle on the floor just below the bottling bucket spigot and slowly drew off a couple of quarts (vorlauf) and carefully poured back into the bucket.
To sparge, I just opened the spigot to a trickle and used a 2 cup measuring cup to scoop water from the pot on the stove and pour gently into the bucket when the water level dropped to keep the water level above the grain. I didn't use the colander when sparging, I just trickled the water out of the cup moving it around to avoid channeling.
After collecting the appropriate amount of water for my recipe, it just became an extract boil.
This was also the first brew where I attempted water correction using salts, "Dublinizing" RO water by adding salts to the grain prior to placing them in the brew kettle for mashing.
My results were outstanding - much better than I expected. I came in just below estimated OG and hit 69% efficiency. More importantly, the beer was better than many commercial stouts. The process was easy and enjoyable. After this one session I knew I'd move to all grain quickly, so I built an MLT and HLT and used them on my next couple of partial mash brews rather than using the "kettle in the oven" process. That said, kettle in the oven was easier and the results were as good, so it's a fine process if you don't plan to move to all grain.
Good luck, and let us know how it turns out.