I would suggest that you snapfreeze your adipose tissue samples until the method of analysis of PPAR gamma and UCP-1 is established. What is the species you want to study? Do you have access to RT-PCR? If yes, I would suggest that you first check mRNA expression of both targets. For UCP-1 in mice, I would also collect brown adipose tissue as a control. However, this is more complicated in humans ...
If u want to do western blot analysis / RTPCR analysis first snap freeze adipose tissue for long storage in -80o. Else, you do have plan to do as soon as animal sacrifice or tissue collection for protein isolation - RIP buffer / sucrose buffer with Protease inhibitor you should homogenate and centrifuge. In case for RNA isolation go with TRIZOL. If you want DNA sample you choose appropriate DNA Isolation buffer and isolate the same. (for each sample preparation you will get protocol). Then you can analysis your protein / mRNA / DNA region of interest PPARg and UCP-1 by immunoblot method, QPCR with specific probe in the form of antibody for immunoblot / primer in case PCR
Snap freezing tissue is highly recommended. For preparation of protein extracts, I use RIPA buffer supplemented with .1% SDS. Addition of SDS will also ensure that nuclei are disrupted, allowing for downstream immunoblotting for PPAR. The recommendation by Henrike to use brown adipose tissue as a positive control for UCP-1 is a really good suggestion. Best of luck with your research.
Samples from liposuction have undergone pretty high stress - I would rather use it for isolation of cells than for gene expression analysis. As for abdominal surgery, quality is perfect if directly processed. Why do you want to measure UCP-1 in your samples? As this is subcutaneous human fat, I would not expect any measurable amount of UCP-1, at least on the protein level. Brown adipose tissue in humans can be used from the neck region to have a positive human control but then you need another type of surgery to get it.