Here's the list of species and transformations that can or cannot be used, just for reference. If you have any ideas of what could be added to the list, please feel free to leave them in the comments.
I was thinking that when doing the gacha, we could simply randomly generate a number and use that to determine the result.
Ben 10 Universe:
Ben 10 - Canon Aliens in the Omnitrix
1 - Four Arms [Tetramand]
2 - Heatblast [Pyronite]
3 - XLR8 [Kineceleran]
4 - Grey Matter [Galvan]
5 - Wildmutt [Vulpimancer]
6 - Stinkfly [Lepidopterran]
7 - Ripjaws [Piscciss Volann]
8 - Upgrade [Galvanic Mechamorph]
9 - Ghostfreak [Ectonurite]
10 - Cannonbolt [Arburian Pelarota]
11 - Wildvine [Florauna]
12 - Blitzwolfer (Wolfen) [Loboan]
13 - Snare-oh [Thep Khufan]
14 - Frankenstrike [Transylian]
15 - Upchuck [Perk Gourmand]
16 - Ditto / Clone [Splixions]
17 - Eye Guy [Oryctini]
18 - Way Big [To'kustar]
19 - Spitter [Orishan]
20 - Buzzshock [Amperi]
21 - Arcticguana [Polar Manzardill]
22 - Big Chill [Ssserpent]
23 - Armadillo [Talpaedan]
24 - Sandstorm [Cascan]
25 - Swampfire [Methanosian]
26 - Echo Echo [Sonorosian]
27 - Humungousaur [Vaxasaurian]
28 - Jetray [Aerophibian]
29 - Big Chill [Necrofriggian]
30 - Chromastone [Crystalsapien]
31 - Spidermonkey [Arachnichimp]
32 - Armodrillo [Piscciss Premann]
33 - Goop [Polymorph]
34 - Alien X [Celestialsapien]
35 - Lodestar [Biosovortian]
36 - Rath [Appoplexian]
37 - Nanomech [Human-Nanochip Fusion]
38 - Water Hazard [Piscciss Volann]
39 - AmpFibian [Mermaid]
40 - Terraspin [Talpaedan]
41 - Fasttrack [Citrakayah]
42 - Clockwork [Chronian]
43 - ChamAlien [Merlinisapien]
44 - Shocksquatch [Gimlinopithecus]
45 - Crashhopper [Oryctini]
46 - Arctiguana [Crustacean]
47 - Feedback [Conductoid]
48 - Bloxx [Segmentasapien]
49 - Gravattack [Galilean]
50 - Ball Weevil [Unknown] - Ballclorosian
51 - Walkatrout [Unknown] - Lewodanian
52 - Pesky Dust [Unknown] - Galilean
53 - Mole-Stache [Ickthyperambuloid]
54 - The Worst [Atrocian]
55 - Astrodactyl [Pturbossaurian]
56 - Spitter [Sphoeroid]
57 - Bullfrag [Inkursian]
58 - Atomix [Unknown] - Nucleartian
59 - Gutrot [Unknown] - Paponionte
60 - Whampire [Vladat]
61 - NRG [Prypiatosian Bs]
62 - Armodrillo [Talpaedan]
63 - Terraspin [Geochelone Aerio]
Ben 10 - Canon Aliens outside the Omnitrix
66 - Anodites
67 - Chronosapiens
68 - DNAliens
69 - Humans
70 - Celestialsapiens
71 - Revonnahganderos
72 - Osmosians
73 - Null Guardians
74 - Limaxes
75 - Sotoraggians
76 - Detrovites
77 - Naljians
78 - Gracklflints
79 - Piscciss Premanns
80 - Galileans
81 - Cabraliens
82 - Kraaho
83 - Chimera Sui Generis
87 - Muroids
88 - Uxorites
89 - Dragons
90 - Maxatomars
91 - Pantophages
92 - Lewodanians
93 - Sylonoids
94 - Dracosians
95 - Protosts
96 - Serpanoids
97 - Thalassians
98 - Antarians
99 - Bulvonians
100 - Zaroffians
101 - Genetometaformos
102 - Snidellerodontus
103 - Ventrilosquid
DC Universe
104 - Kryptonians
105 - Thanagarians
106 - Tamaraneans
107 - Coluans
108 - Martians
109 - Daxamites
110 - Okaarians
111 - Czarnians
112 - Psions
113 - Khunds
114 - Rannians
115 - Rann-Thanagarians
116 - Carggites
117 - Angorians
118 - Gordanians
119 - Xudarians
120 - Dominators
121 - Vega
122 - Graxosians
123 - Bolovaxians
124 - Takron-Galtosians
125 - Almeracians
126 - Braalians
127 - Barndanes
128 - Kroloteans
129 - Ruling Elite of Rann
130 - Sarnians
131 - Ranxians
132 - Rimborians
133 - Glorithians
134 - Apokoliptians
135 - New Gods of New Genesis
136 - Anti-Monitor's Warriors
137 - Oans 138 - Maltusians
139 - Amalakians
140 - Psycopirates
141 - Dhorians
142 - Vulcanians
Marvel Universe
143 - Kree
144 - Skrulls
145 - Shi'ar
146 - Celestials
147 - Chitauri
148 - Brood
149 - Sakaarians
150 - Dire Wraiths
151 - Badoon
152 - Phalanx
153 - Korbinites
154 - Spartax
155 - Centaurians
156 - Inhumans
157 - Axi-Tun
158 - Rigellians
159 - Kymellians
160 - Ariguans
161 - Luminals
162 - Klyntar (Symbiotes)
163 - Xandarians
164 - Acanti
165 - Aakon
166 - Dire Wraiths
167 - Diregoes
168 - Mutant Korbinites
169 - Lemurians
170 - Mercurians
171 - Orollans
172 - Eternals
173 - Deviants
174 - Alpha Primitives
Star Wars Universe
175 - Wookiees
176 - Hutts
177 - Twi'leks
178 - Rodians
179 - Bothans
180 - Trandoshans
181 - Mon Calamari
182 - Ewoks
183 - Jawas
184 - Tusken Raiders
185 - Gamorreans
186 - Zabraks
187 - Mandalorians
188 - Chiss
189 - Dathomirians
190 - Gungans
191 - Neimoidians
192 - Geonosians
193 - Quarren
194 - Ithorians
195 - Sullustans
196 - Mirialans
197 - Kaleesh
198 - Zeltrons
199 - Toydarians
200 - Kaminoans
201 - Echani
202 - Biths
203 - Wampas
204 - Tauntauns
205 - Yuzzums
206 - Ugnaughts
207 - Aqualish
208 - Harch
209 - Iktotchis
210 - Umbarans
211 - Togrutans
RPG Races
212 - Elves
213 - Dwarves
214 - Orcs
215 - Gnomes
216 - Halflings
217 - Goblins
218 - Trolls
219 - Fairies
220 - Centaurs
221 - Minotaurs
222 - Vampires
223 - Werewolves
224 - Dragonborn
225 - Tieflings
226 - Aarakocra
227 - Genasi
228 - Genies
229 - Shifters
230 - Warforged
231 - Kenku
232 - Tabaxi
233 - Tritons
234 - Yuan-ti
235 - Githyanki
236 - Githzerai
237 - Sahuagin
238 - Lizardfolk
239 - Gnolls
240 - Bugbears
241 - Hobgoblins
242 - Kuo-toa
243 - Goblins
244 - Kobolds
245 - Tritons