Without knowing any more about what kind of detox, I'm going to assume you talking about a general overall cleanse.
Lemon water in the morning is fantastic. It sounds overly simplistic, but the vitamin/mineral content is great, the alkalizing effects are impressive, and it aids both liver and kidney function. Since the liver and kidneys are primary detoxification organs, supporting their actions is a natural.
Cranberry used in small quantities is excellent as it increases urinary output which will facilitate kidney function. Juice them for best results or use Knudsen or Lakewood brands of truly pure cranberry. Add an ounce of cranberry juice to about 3 ounces of water. If sweetener is desired, consider using stevia, xylitol, or raw honey.
Plants that work well with a juice detox include anything that is rich in chlorophyll, anything that has a rich green color, the darker the better; kale, collards, romaine, greens (from beets, mustard, carrots, etc.). Chlorophyll works to purify the blood and, like the lemon water, helps to balance pH. Herbs included in this list would be alfalfa, nettles, aloe vera (barbadensis miller variety) and dandelion greens.
The aloe vera in particular is awesome. I have done many detoxes using aloe as a primary assist and have always seen good results without bombing myself with detox symptoms. Make sure to use a really good quality aloe vera juice or if juicing your own, try to use only aloe vera barbadensis miller. It doesn't have the laxative properties other species have. You don't want to have to lock yourself in a bathroom the whole time your "enjoying" your detox.
Best aloe I've used is from the company Aloe Life but I also get great results from Lily of the Desert. Lily costs less, but if price isn't a big deal, try to find Aloe Life, their aloe is awesome.
Straight up herbs that aid natural detoxification would include milk thistle, dandelion, schizandra, turmeric, garlic, and ginger. Ginger isn't so specifically detoxifying, but will help with digestive comfort, circulation, and assimilation of the other herbs and foods. If you like spicy tastes, you could also add in a bit of cayenne juice or cayenne powder. Cayenne also serves as a delivery system for the other herbs and foods.
I have more information about juicing/detox on my website. It's link is in my profile under contact info.
I've done a few colon and general cleansing/detoxifications and found the advice to ensure sufficient water intake the most relevant. (It is suggested that we drink 1/2 our body weight in ounces every day, not just when specifically on a special cleanse program.)
The vegetable juicing will really help you give your body the nutrients it needs, keeping your diet simple during a detox and getting as much rest as you can are key to a successful detox.
Understand that when you detox the body most of the time feels worst before it feels better. I did a 45 day juice fast which helped me to lose 26 pounds and 7 dress sizes. I used Barlean's lemon zest omega swirl fish oil and took extra vitamin D 5,000 IU's. I also took the supplements that you are taking but one of the biggest things that I drank for lunch which I found made a big difference is Kambucha; this helped to curb my hunger and it is raw. Good luck with your juice fast.