Forge 1180, CCC 1.0.1.8, Project Red 4.4.5 with Base and Mechanical. Base alone and with Lighting works.
Minecraft gave me this:

---- Minecraft Crash Report ----
// Quite honestly, I wouldn't worry myself about that.

Time: 8/16/14 1:37 PM
Description: There was a severe problem during mod loading that has caused the game to fail

cpw.mods.fml.common.LoaderException: java.lang.NoClassDefFoundError: mrtjp/projectred/transmission/PowerWire100v
at cpw.mods.fml.common.LoadController.transition(LoadController.java:162)
at cpw.mods.fml.common.Loader.preinitializeMods(Loader.java:515)
at cpw.mods.fml.client.FMLClientHandler.beginMinecraftLoading(FMLClientHandler.java:239)
at net.minecraft.client.Minecraft.func_71384_a(Minecraft.java:480)
at net.minecraft.client.Minecraft.func_99999_d(Minecraft.java:867)
at net.minecraft.client.main.Main.main(SourceFile:148)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at net.minecraft.launchwrapper.Launch.launch(Launch.java:134)
at net.minecraft.launchwrapper.Launch.main(Launch.java:28)
Caused by: java.lang.NoClassDefFoundError: mrtjp/projectred/transmission/PowerWire100v
at mrtjp.projectred.ProjectRedExpansion$.preInit(ProjectRedExpansion.scala:28)
at mrtjp.projectred.ProjectRedExpansion.preInit(ProjectRedExpansion.scala)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at cpw.mods.fml.common.FMLModContainer.handleModStateEvent(FMLModContainer.java:513)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74)
at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304)
at com.google.common.eventbus.EventBus.post(EventBus.java:275)
at cpw.mods.fml.common.LoadController.sendEventToModContainer(LoadController.java:208)
at cpw.mods.fml.common.LoadController.propogateStateMessage(LoadController.java:187)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(NativeMethodAccessorImpl.java:57)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(DelegatingMethodAccessorImpl.java:43)
at java.lang.reflect.Method.invoke(Method.java:606)
at com.google.common.eventbus.EventSubscriber.handleEvent(EventSubscriber.java:74)
at com.google.common.eventbus.SynchronizedEventSubscriber.handleEvent(SynchronizedEventSubscriber.java:47)
at com.google.common.eventbus.EventBus.dispatch(EventBus.java:322)
at com.google.common.eventbus.EventBus.dispatchQueuedEvents(EventBus.java:304)
at com.google.common.eventbus.EventBus.post(EventBus.java:275)
at cpw.mods.fml.common.LoadController.distributeStateMessage(LoadController.java:118)
at cpw.mods.fml.common.Loader.preinitializeMods(Loader.java:513)
... 10 more
Caused by: java.lang.ClassNotFoundException: mrtjp.projectred.transmission.PowerWire100v
at net.minecraft.launchwrapper.LaunchClassLoader.findClass(LaunchClassLoader.java:188)
at java.lang.ClassLoader.loadClass(ClassLoader.java:425)
at java.lang.ClassLoader.loadClass(ClassLoader.java:358)
... 39 more
Caused by: java.lang.NullPointerException

A detailed walkthrough of the error, its code path and all known details is as follows:

-- System Details --
Details:
Minecraft Version: 1.7.10
Operating System: Linux (amd64) version 3.13.0-34-generic
Java Version: 1.7.0_55, Oracle Corporation
Java VM Version: OpenJDK 64-Bit Server VM (mixed mode), Oracle Corporation
Memory: 102053608 bytes (97 MB) / 260624384 bytes (248 MB) up to 1060372480 bytes (1011 MB)
JVM Flags: 5 total; -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M
AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
FML: MCP v9.05 FML v7.10.18.1180 Minecraft Forge 10.13.0.1180 10 mods loaded, 10 mods active
mcp{9.05} Minecraft Coder Pack Unloaded->Constructed->Pre-initialized
FML{7.10.18.1180} Forge Mod Loader Unloaded->Constructed->Pre-initialized
Forge{10.13.0.1180} Minecraft Forge Unloaded->Constructed->Pre-initialized
CodeChickenCore{1.0.1.8} CodeChicken Core Unloaded->Constructed->Pre-initialized
ForgeMultipart{1.1.0.296} Forge Multipart Unloaded->Constructed->Pre-initialized
ProjRed|Core{4.4.5.44} ProjectRed Unloaded->Constructed->Pre-initialized
ProjRed|Expansion{4.4.5.44} ProjectRed-Expansion Unloaded->Constructed->Errored
ProjRed|Transportation{4.4.5.44} ProjectRed-Transportation Unloaded->Constructed->Errored
McMultipart{1.1.0.296} Minecraft Multipart Plugin Unloaded->Constructed->Pre-initialized
ForgeMicroblock{1.1.0.296} Forge Microblocks Unloaded->Constructed->Pre-initialized

That works; thanks!

Looks like you need the Integration jar. Mech has a dependency on it.