The closest thing to anthropomorphic characters are changelings, detailed in the Runner's Companion sourcebook. For a character to be a changeling, they have to take a SURGE quality, in one of three levels (I, II, and III, costing 5, 10, and 15 BP, respectively) which grants them access to a number of metagenetic qualities. SURGE I grants 10 BP of positive and 5 BP of negative qualities, II grants 20 positive and 10 negative, and III grants 30 positive and 15 negative. For a character as anthropomorphic as yours, you'd want to take SURGE III. The qualities, however, are quite varied, and many of them can be replicated with the cyber, bio, and gene mods found in the Augmentation sourcebook. You'd have to decide which ones you want naturally and which ones you want modified.
For example, you'll probably want something that alters your fur. You can take this in many forms: SURGE has two classes of fur qualities: functional and non-functional. Functional furs offer a physical bonus, like Quills, Insulating Pelt, and Camo Fur. Their cost varies from 5-10 BP. Non-functional fur is called Unusual Hair, and can range from simple lion's manes to full-bodied fur, and is a 5 BP negative metagenetic quality. Cyberware offers cyberlimb casemods, which alter the appearance of cyberlimbs, allowing you to cover one in fake tiger fur, as well as the vague "cosmetic modification" found in the corebook that costs between 200-10,000 nuyen and specifically lists things like fiber optic fur and tails. Bioware offers a hair growth mod, which at 500 nuyen per human-head-sized coverage, is a relatively cheap alternative with no essence cost. Finally, geneware offers the simple and holistic animal features transgenic alteration, costing upwards of 45,000 nuyen and .3 essence, but if you're going to spend at least 9 BP in resources for a cosmetic modification, you might as well take it as a metagenetic quality and
earn yourself 5 BP.
If you want a tail, you have a few options as well. Just like fur, SURGE offers functional and non-functional tails: The Balance Tail costs 5 BP and grants a couple bonus dice to some tests involving keeping your balance. The Vestigial Tail grants 5 BP with no effective function other than wagging. You can also get a cyber balance tail, with fake fur available. With bioware, you can get severe cosmetic modification surgery, but there is no cost listed for it.
If you want to use your claws and fangs as weapons, there are also several options. Claws are a 5 BP positive metagenetic quality, with Retractable ones costing 5 BP more. Fangs also cost 5 BP. Cyberware fang implants are cheap and have a slightly more expensive retractable option, and retractable hand razors/spurs can act like claws and can be implanted straight into a natural armor or installed into a cyberlimb.
For those cool tiger eyes, you can take the SURGE negative metagenetic quality Unusual Eyes for 5 BP (a cheap cop-out is to just buy a pair of contacts or mirrorshades to overcome that negative social dice pool modifier, but with the rest of you being so modified anyway, your GM will probably be imposing one anyway). You can get a cosmetic eyemod for your cybereyes on the cheap, as well. You may also get implanted with bioware cat eyes that grant you low-light vision.
For all of the other benefits a tiger may be granted, like enhanced hearing and olfactory abilities, these can be purchased with SURGE and cyber/bioware as you see fit. Don't forget the other combat benefits that SURGE can provide like increased attributes.
With this in mind, it is up to you to decide how many SURGE qualities and/or cyber/bio modifications that you want to take. Your decision should be guided in part by the character's flavor and by what you want him/her to do. If you plan on being a melee adept, you should probably take SURGE over wares. If you want to be a mundane street samurai, wares might be a better alternative.
I'll leave you with a cyberware suite (rules found in Augmentation):
Xevozcorp Tygar Combat Cyberware Suite: 30,000 nuyen, 1.575 essence
Xevozcorp has been dedicated to developing and producing cyberware modifications that allow consumers to live the anthropomorphic fantasies that they desire. The popularity of these modifications among consumers interested in the field of private security has lead them to design various combat suites to allow them to use the might of their chosen animal in their line of work. The Tygar suite was designed for those who wish to have the grace, elegance, and utter ferocity of a tiger.
- Spoiler:
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R2 Cybereyes (Feline Eye Cosmetic Modification)
+R3 Vision Enhancement
+Vision Magnification
+Low-Light Vision
+Flare Compensation
R2 Cyberears (Feline Ear Cosmetic Modification) (I charged this cosmod the same as the eye's mod since cybereyes and ears are so similar cost-wise)
+R2 Audio Enhancement
+Increased Sensitivity
+Damper
+Balance Augmenter
R3 Olfactory Booster (Feline Nose Cosmetic Modification) (I charged 2,100 to round the total cost up to 30,000)
Retractable Fang Implants
Balance Tail (Tiger Tail Cosmetic Modification) (Cosmod is free)
Retractable Cyberspur
p.s. I loved Xevoz.