This is a list of the herbs in the 3rd edition of Bensky's Chinese Herbal Medicine Materia Medica which are easiest to grow (at Mountain Gardens); i.e. those which you only have to plant once.  Not all are 'trouble-free' however, many will require some restraining.
Weedy means the plant produces too many seedlings (control by deadheading before the seeds are released)
Invasive means spreads by roots (like mint), these can be contained, or kept under control by harvesting.

Abutilon theophrastii qing ma zi 300 annual; self-sows and may be weedy, esp. in warm areas
Achyranthes bidentata huai niu xi 213 perennial; weedy
Acorus calamus shi chang pu 956 perennial; easy in moist to wet soil, spreads by rhizomes
Agastache rugosa huo xiang 476 annual, bien. or short-lived perennial; self-sows
Agrimonia pilosa xian he cao 584 perennial; weedy
Akebia quinata mu tong 283 strong perennial vine; invasive by rhizomes and rooting stems
Albizia julibrissin he huan pi / hua              935, 937 weed tree' in warm areas
Allium tuberosum jiu cai zi 807 perennial, may be weedy
Ampelopsis japonica bai lian 214 strong perennial vine; weedy and invasive
Angelica dahurica bai zhi 24 biennial; self-sows
Arctium lappa niu bang zi 49 biennial; self-sows
Artemisia annua qing hao 219 annual; weedy
Artemisia argyi ai ye 594 perennial; invasive
Artemisia japonica mu hao 221 perennial; invasive
Artemisia princeps kui hao 596 perennial; invasive
Aster tataricus zi wan 440 perennial; invasive
Begonia fimbristipulata hong tian kui 170 perennial; self sows in partial shade
Bidens bipinnata gui zhen cao 359 annual; weedy
Bidens tripartita lang ba cao 359 annual; weedy
Broussonetia papyrifera gou shu              452, 852 small tree; spreads by rhizomes
Bupleurum chinense chai hu 73 perennial; self-sows in dry / well-drained soil
Campsis radicans ling xiao hua 663 strong perennial vine; invasive by rhizomes and rooting stems
Carpesium abrotanoides he shi          1001, 1003 annual; self-sows
Chrysanthemum morifolium ju hua 58 perennial; clump enlarges by short rhizomes
Clerodendron trichotomum chou wu tong 359 large shrub; invasive
Cnidium monnieri she chuan zi 1025 annual; weedy
Cocculus orbiculatus mu fang ji 315 perennial herbaceous vine; invasive
Codonopsis pilosula dang shen 714 perennial herbaceous vine; self-sows
Commelina communis ya zhi cao 99 common annual weed
Cyperus rotundus xiang fu 527 weedy perennial sedge
Daucus carota ye hu luo bo    19, 1002, 1027 queen anne's lace'; common biennial weed
Dioscorea opposita shan yao 723 air potato' - herbaceous perennial vine, weedy by aerial bulblets
Dioscorea tokoro shan bi xie 303 herbaceous perennial vine; potentially weedy (by seed)
Dipsacus japonicus xu duan 795 biennial; self-sows
Eclipta alba / prostrata han lian cao 836 annual; weedy in moist to wet soil
Elsholtzia ciliata (tu) xiang ru 39 annual; weedy
Epimedium koreanum yin yang huo 776 perennial; clump enlarges by short rhizomes
Equisetum hiemale mu zei 69 perennial; invasive in moist to wet soil
Euonymus alatus wei mao 668 shrub; self-sows
Euphorbia helioscopia ze qi 406 annual; weedy
Foeniculum vulgare xiao hui xiang 697 perennial; self-sows
Forsythia suspensa lian qiao 152 arching shrub, stems may tip-root
Galium verum peng zi cao 567 perennial
Geranium carolinianum ye lao guan cao 342 annual; self-sows
Glechoma longituba huo xue dan              305, 306 perennial; spreads rapidly by runners
Houttynia cordata yu xing cao 176 perennial; invasive, esp. in moist soil
Isatis tinctoria / indigotica song lan 156 biennial; self-sows
Juncus effusus deng xin cao 287 perennial; may be weedy
Kochia scoparia di fu zi 294 annual
Leonurus heterophyllus / sibiricus yi mu cao 616 annual or biennial; weedy
Ligustrum lucidum niu zhen zi 191 deciduous shrub or tree; weedy in SE US
Lonicera japonica jin yin hua              148, 151 herbaceous perennial vine; notoriously invasive
Lycium chinense gou qi zi              222, 760 deciduous arching shrub; spreads by rhizomes & tip-rooting
Malva crispa dong kui 298 annual; self-sows, may be weedy
Malva verticillata ye kui              298, 300 annual to short-lived perennial; self-sows, may be weedy
Ophiopogon japonicus mai men dong 825 perennial; clump enlarges by short rhizomes
Papaver somniferum ying su 1045 winter annual; self-sows, may be weedy
Perilla frutescens zi su ye / zi 12 annual; weedy
Periploca sepium xiang jia pi 340 herbaceous perennial vine; invasive
Phragmites communis lu gen 106 perennial; invasive in moist to wet soil
Phytolacca americana chui xu shang lu 261 perennial; potentially weedy
Pinellia ternata ban xia 413 perennial; weedy
Plantago asiatica che qian 277 perennial; weedy
Plantago lanceolata chang ye che qian 280 perennial; weedy
Plantago major da ye che qian 280 perennial; weedy
Polygonum aviculare bian xu 291 annual; weedy
Polygonum cuspidatum hu zhang 572 perennial; weedy, clump enlarges by short rhizomes
Polygonum multiflorum he shou wu 744 strong herbaceous perennial vine; invasive
Portulaca oleracea ma chi xian 191 annual; weedy
Prunella vulgaris xia ku cao 102 perennial; weedy
Pueraria lobata ge gen 70 strong herbaceous perennial vine; invasive
Rehmannia glutinosa sheng / shu di huang              120, 742 perennial; spreads by rhizomes on sandy / well-drained soil
Rosa rugosa mei gui 542 herbaceous shrub, clump increases by short rhizomes
Rubia cordifolia qian cao 564 perennial; clump enlarges by short rhizomes
Rubus idaeus fu pen zi 889 rasberry'; invasive
Schizonepeta tenuifolia jing jie 14 annual; self-sows
Sedum sarmentosum chui pen cao 201 perennial; clump enlarges by short rhizomes
Siegesbeckia orientalis xi xian 357 annual; self-sows
Siegesbeckia pubescens xian geng xi xian 357 annual; self-sows
Sinapis alba bai jie 423 annual; self-sows
Solanum nigrum long kui 171 perennial
Thlaspi arvense xi ming (su bai jiang) 175 winter annual; self-sows, may be weedy
Torilis japonica qie yi 1002 annual; weedy
Tribulus terrestris (ci) ji li 973 weedy on sandy soil (beach)
Trichosanthes kirilowii tian hua fen, gua luo pi  108,383,386,388 strong perennial herbaceous vine; invasive. Dioecious - needs both male & female plants (and heat) to fruit
Tussilago farfara kuan dong hua 442 perennial; invasive and may be weedy on moist to wet soil
Typhonium giganteum zhi bai fu zi 421 perennial; weedy